Find missing angles in quadrilaterals using the rule that the sum of interior angles is 360°.
Worksheet titled "Missing Angles in a Quadrilateral 1" with eight problems showing quadrilaterals and angles, asking to find the missing angle values using the property that interior angles sum to 360°.
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Step-by-step solution for: Missing Angles in Quadrilaterals 1 online exercise for | Live ...
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Show Answer Key & Explanations
Step-by-step solution for: Missing Angles in Quadrilaterals 1 online exercise for | Live ...
To solve the problem of finding the missing angles in each quadrilateral, we will use the fact that the sum of the interior angles of a quadrilateral is always 360°. Let's go through each problem step by step.
---
The quadrilateral has one right angle (90°), another right angle (90°), and one given angle (75°). We need to find the missing angle marked with "?".
#### Steps:
1. Sum of interior angles of a quadrilateral: \( 360^\circ \)
2. Known angles: \( 90^\circ + 90^\circ + 75^\circ = 255^\circ \)
3. Missing angle: \( 360^\circ - 255^\circ = 105^\circ \)
#### Answer:
\[ \boxed{105^\circ} \]
---
The quadrilateral has angles of \( 84^\circ \), \( 50^\circ \), and \( 146^\circ \). We need to find the missing angle marked with "?".
#### Steps:
1. Sum of interior angles of a quadrilateral: \( 360^\circ \)
2. Known angles: \( 84^\circ + 50^\circ + 146^\circ = 280^\circ \)
3. Missing angle: \( 360^\circ - 280^\circ = 80^\circ \)
#### Answer:
\[ \boxed{80^\circ} \]
---
The quadrilateral has angles of \( 52^\circ \), \( 43^\circ \), and \( 128^\circ \). We need to find the missing angle marked with "?".
#### Steps:
1. Sum of interior angles of a quadrilateral: \( 360^\circ \)
2. Known angles: \( 52^\circ + 43^\circ + 128^\circ = 223^\circ \)
3. Missing angle: \( 360^\circ - 223^\circ = 137^\circ \)
#### Answer:
\[ \boxed{137^\circ} \]
---
The quadrilateral is a parallelogram (opposite angles are equal, and adjacent angles are supplementary). One angle is given as \( 78^\circ \).
#### Steps:
1. In a parallelogram, opposite angles are equal. So, the angle opposite to \( 78^\circ \) is also \( 78^\circ \).
2. Adjacent angles in a parallelogram are supplementary. Therefore, the other two angles are:
\[
180^\circ - 78^\circ = 102^\circ
\]
3. Both missing angles are \( 102^\circ \).
#### Answer:
\[ \boxed{102^\circ} \]
---
The quadrilateral is a rectangle (all angles are right angles, i.e., \( 90^\circ \)). One angle is given as \( 67^\circ \).
#### Steps:
1. In a rectangle, all angles are \( 90^\circ \). The given angle \( 67^\circ \) is not relevant here because it does not affect the interior angles of the rectangle.
2. The missing angle is simply \( 90^\circ \).
#### Answer:
\[ \boxed{90^\circ} \]
---
The quadrilateral has angles of \( 47^\circ \), \( 128^\circ \), and \( 86^\circ \). We need to find the missing angle marked with "?".
#### Steps:
1. Sum of interior angles of a quadrilateral: \( 360^\circ \)
2. Known angles: \( 47^\circ + 128^\circ + 86^\circ = 261^\circ \)
3. Missing angle: \( 360^\circ - 261^\circ = 99^\circ \)
#### Answer:
\[ \boxed{99^\circ} \]
---
The quadrilateral is a rhombus. It has angles of \( 34^\circ \), \( 146^\circ \), and \( 34^\circ \). We need to find the missing angle marked with "?".
#### Steps:
1. In a rhombus, opposite angles are equal. So, the angle opposite to \( 34^\circ \) is also \( 34^\circ \).
2. The sum of interior angles of a quadrilateral is \( 360^\circ \).
3. Known angles: \( 34^\circ + 146^\circ + 34^\circ = 214^\circ \)
4. Missing angle: \( 360^\circ - 214^\circ = 146^\circ \)
#### Answer:
\[ \boxed{146^\circ} \]
---
The quadrilateral has angles of \( 23^\circ \), \( 234^\circ \), and a right angle (\( 90^\circ \)). We need to find the missing angle marked with "?".
#### Steps:
1. Sum of interior angles of a quadrilateral: \( 360^\circ \)
2. Known angles: \( 23^\circ + 234^\circ + 90^\circ = 347^\circ \)
3. Missing angle: \( 360^\circ - 347^\circ = 13^\circ \)
#### Answer:
\[ \boxed{13^\circ} \]
---
\[
\boxed{105^\circ, 80^\circ, 137^\circ, 102^\circ, 90^\circ, 99^\circ, 146^\circ, 13^\circ}
\]
---
1)
The quadrilateral has one right angle (90°), another right angle (90°), and one given angle (75°). We need to find the missing angle marked with "?".
#### Steps:
1. Sum of interior angles of a quadrilateral: \( 360^\circ \)
2. Known angles: \( 90^\circ + 90^\circ + 75^\circ = 255^\circ \)
3. Missing angle: \( 360^\circ - 255^\circ = 105^\circ \)
#### Answer:
\[ \boxed{105^\circ} \]
---
2)
The quadrilateral has angles of \( 84^\circ \), \( 50^\circ \), and \( 146^\circ \). We need to find the missing angle marked with "?".
#### Steps:
1. Sum of interior angles of a quadrilateral: \( 360^\circ \)
2. Known angles: \( 84^\circ + 50^\circ + 146^\circ = 280^\circ \)
3. Missing angle: \( 360^\circ - 280^\circ = 80^\circ \)
#### Answer:
\[ \boxed{80^\circ} \]
---
3)
The quadrilateral has angles of \( 52^\circ \), \( 43^\circ \), and \( 128^\circ \). We need to find the missing angle marked with "?".
#### Steps:
1. Sum of interior angles of a quadrilateral: \( 360^\circ \)
2. Known angles: \( 52^\circ + 43^\circ + 128^\circ = 223^\circ \)
3. Missing angle: \( 360^\circ - 223^\circ = 137^\circ \)
#### Answer:
\[ \boxed{137^\circ} \]
---
4)
The quadrilateral is a parallelogram (opposite angles are equal, and adjacent angles are supplementary). One angle is given as \( 78^\circ \).
#### Steps:
1. In a parallelogram, opposite angles are equal. So, the angle opposite to \( 78^\circ \) is also \( 78^\circ \).
2. Adjacent angles in a parallelogram are supplementary. Therefore, the other two angles are:
\[
180^\circ - 78^\circ = 102^\circ
\]
3. Both missing angles are \( 102^\circ \).
#### Answer:
\[ \boxed{102^\circ} \]
---
5)
The quadrilateral is a rectangle (all angles are right angles, i.e., \( 90^\circ \)). One angle is given as \( 67^\circ \).
#### Steps:
1. In a rectangle, all angles are \( 90^\circ \). The given angle \( 67^\circ \) is not relevant here because it does not affect the interior angles of the rectangle.
2. The missing angle is simply \( 90^\circ \).
#### Answer:
\[ \boxed{90^\circ} \]
---
6)
The quadrilateral has angles of \( 47^\circ \), \( 128^\circ \), and \( 86^\circ \). We need to find the missing angle marked with "?".
#### Steps:
1. Sum of interior angles of a quadrilateral: \( 360^\circ \)
2. Known angles: \( 47^\circ + 128^\circ + 86^\circ = 261^\circ \)
3. Missing angle: \( 360^\circ - 261^\circ = 99^\circ \)
#### Answer:
\[ \boxed{99^\circ} \]
---
7)
The quadrilateral is a rhombus. It has angles of \( 34^\circ \), \( 146^\circ \), and \( 34^\circ \). We need to find the missing angle marked with "?".
#### Steps:
1. In a rhombus, opposite angles are equal. So, the angle opposite to \( 34^\circ \) is also \( 34^\circ \).
2. The sum of interior angles of a quadrilateral is \( 360^\circ \).
3. Known angles: \( 34^\circ + 146^\circ + 34^\circ = 214^\circ \)
4. Missing angle: \( 360^\circ - 214^\circ = 146^\circ \)
#### Answer:
\[ \boxed{146^\circ} \]
---
8)
The quadrilateral has angles of \( 23^\circ \), \( 234^\circ \), and a right angle (\( 90^\circ \)). We need to find the missing angle marked with "?".
#### Steps:
1. Sum of interior angles of a quadrilateral: \( 360^\circ \)
2. Known angles: \( 23^\circ + 234^\circ + 90^\circ = 347^\circ \)
3. Missing angle: \( 360^\circ - 347^\circ = 13^\circ \)
#### Answer:
\[ \boxed{13^\circ} \]
---
Final Answers:
\[
\boxed{105^\circ, 80^\circ, 137^\circ, 102^\circ, 90^\circ, 99^\circ, 146^\circ, 13^\circ}
\]
Parent Tip: Review the logic above to help your child master the concept of quadrilateral angle worksheet.