To solve the problem of finding the missing angles in each diagram, we will use the following key principles:
1.
Angles in a triangle sum to 180°.
2.
A straight line forms an angle of 180°.
3.
Angles around a point sum to 360°.
4.
A right angle is 90°.
Let's solve each part step by step.
---
Problem 1:
The diagram shows a right triangle with one angle given as 70°. We need to find the missing angle.
- The triangle has a right angle (90°) and another angle (70°).
- The sum of angles in a triangle is 180°.
- Let the missing angle be \( x \).
\[
90^\circ + 70^\circ + x = 180^\circ
\]
\[
160^\circ + x = 180^\circ
\]
\[
x = 180^\circ - 160^\circ = 20^\circ
\]
Answer for Problem 1: \( \boxed{20^\circ} \)
---
Problem 2:
The diagram shows a straight line with one angle given as 40°. We need to find the missing angle.
- A straight line forms an angle of 180°.
- Let the missing angle be \( x \).
\[
40^\circ + x = 180^\circ
\]
\[
x = 180^\circ - 40^\circ = 140^\circ
\]
Answer for Problem 2: \( \boxed{140^\circ} \)
---
Problem 3:
The diagram shows a right triangle with one angle given as 40°. We need to find the missing angle.
- The triangle has a right angle (90°) and another angle (40°).
- The sum of angles in a triangle is 180°.
- Let the missing angle be \( x \).
\[
90^\circ + 40^\circ + x = 180^\circ
\]
\[
130^\circ + x = 180^\circ
\]
\[
x = 180^\circ - 130^\circ = 50^\circ
\]
Answer for Problem 3: \( \boxed{50^\circ} \)
---
Problem 4:
The diagram shows an isosceles triangle with two base angles given as 35° each. We need to find the missing angle at the top.
- In an isosceles triangle, the base angles are equal.
- The sum of angles in a triangle is 180°.
- Let the missing angle be \( x \).
\[
35^\circ + 35^\circ + x = 180^\circ
\]
\[
70^\circ + x = 180^\circ
\]
\[
x = 180^\circ - 70^\circ = 110^\circ
\]
Answer for Problem 4: \( \boxed{110^\circ} \)
---
Problem 5:
The diagram shows angles around a point with two angles given as 55° and 200°. We need to find the missing angle.
- Angles around a point sum to 360°.
- Let the missing angle be \( x \).
\[
55^\circ + 200^\circ + x = 360^\circ
\]
\[
255^\circ + x = 360^\circ
\]
\[
x = 360^\circ - 255^\circ = 105^\circ
\]
Answer for Problem 5: \( \boxed{105^\circ} \)
---
Problem 6:
The diagram shows a triangle with two angles given as 33° and 68°. We need to find the missing angle.
- The sum of angles in a triangle is 180°.
- Let the missing angle be \( x \).
\[
33^\circ + 68^\circ + x = 180^\circ
\]
\[
101^\circ + x = 180^\circ
\]
\[
x = 180^\circ - 101^\circ = 79^\circ
\]
Answer for Problem 6: \( \boxed{79^\circ} \)
---
Final Answers:
1. \( \boxed{20^\circ} \)
2. \( \boxed{140^\circ} \)
3. \( \boxed{50^\circ} \)
4. \( \boxed{110^\circ} \)
5. \( \boxed{105^\circ} \)
6. \( \boxed{79^\circ} \)
Parent Tip: Review the logic above to help your child master the concept of geometric angles worksheets.
