To solve for the missing angle labeled \( \alpha \) in each triangle, we use the fact that the sum of the interior angles of a triangle is always
180°. Let's solve each problem step by step.
---
1. Scalene Triangle
Given angles: \( 45^\circ \) and \( 75^\circ \)
The sum of the angles in a triangle is:
\[
\alpha + 45^\circ + 75^\circ = 180^\circ
\]
Simplify:
\[
\alpha + 120^\circ = 180^\circ
\]
Solve for \( \alpha \):
\[
\alpha = 180^\circ - 120^\circ = 60^\circ
\]
Answer:
\[
\boxed{60^\circ}
\]
---
2. Isosceles Triangle
Given angles: \( 110^\circ \) and two equal angles (since it is isosceles).
Let the two equal angles be \( \alpha \). The sum of the angles in a triangle is:
\[
\alpha + \alpha + 110^\circ = 180^\circ
\]
Simplify:
\[
2\alpha + 110^\circ = 180^\circ
\]
Solve for \( \alpha \):
\[
2\alpha = 180^\circ - 110^\circ = 70^\circ
\]
\[
\alpha = \frac{70^\circ}{2} = 35^\circ
\]
Answer:
\[
\boxed{35^\circ}
\]
---
3. Right Triangle
Given angles: \( 90^\circ \) (right angle) and \( 60^\circ \)
The sum of the angles in a triangle is:
\[
\alpha + 90^\circ + 60^\circ = 180^\circ
\]
Simplify:
\[
\alpha + 150^\circ = 180^\circ
\]
Solve for \( \alpha \):
\[
\alpha = 180^\circ - 150^\circ = 30^\circ
\]
Answer:
\[
\boxed{30^\circ}
\]
---
4. Scalene Triangle
Given angles: \( 70^\circ \) and \( 30^\circ \)
The sum of the angles in a triangle is:
\[
\alpha + 70^\circ + 30^\circ = 180^\circ
\]
Simplify:
\[
\alpha + 100^\circ = 180^\circ
\]
Solve for \( \alpha \):
\[
\alpha = 180^\circ - 100^\circ = 80^\circ
\]
Answer:
\[
\boxed{80^\circ}
\]
---
5. Isosceles Triangle
Given angles: \( 40^\circ \) and two equal angles (since it is isosceles).
Let the two equal angles be \( \alpha \). The sum of the angles in a triangle is:
\[
\alpha + \alpha + 40^\circ = 180^\circ
\]
Simplify:
\[
2\alpha + 40^\circ = 180^\circ
\]
Solve for \( \alpha \):
\[
2\alpha = 180^\circ - 40^\circ = 140^\circ
\]
\[
\alpha = \frac{140^\circ}{2} = 70^\circ
\]
Answer:
\[
\boxed{70^\circ}
\]
---
6. Right Triangle
Given angles: \( 90^\circ \) (right angle) and \( 65^\circ \)
The sum of the angles in a triangle is:
\[
\alpha + 90^\circ + 65^\circ = 180^\circ
\]
Simplify:
\[
\alpha + 155^\circ = 180^\circ
\]
Solve for \( \alpha \):
\[
\alpha = 180^\circ - 155^\circ = 25^\circ
\]
Answer:
\[
\boxed{25^\circ}
\]
---
Final Answers:
1. \( \boxed{60^\circ} \)
2. \( \boxed{35^\circ} \)
3. \( \boxed{30^\circ} \)
4. \( \boxed{80^\circ} \)
5. \( \boxed{70^\circ} \)
6. \( \boxed{25^\circ} \)
Parent Tip: Review the logic above to help your child master the concept of isosceles triangle worksheet.
