To solve the problem of finding the missing angles in the triangles, we use the fundamental property of triangles:
the sum of the interior angles of a triangle is always 180°. Let's go through each part step by step.
---
a)
The given angles are:
- One angle = 50°
- Another angle = 80°
To find the missing angle:
\[
\text{Missing angle} = 180° - (50° + 80°) = 180° - 130° = 50°
\]
Answer for part (a):
\[
\boxed{50°}
\]
---
b)
The given angle is:
- One angle = 110°
Since this is an exterior angle, it is equal to the sum of the two non-adjacent interior angles. However, if we assume this is a typo and the triangle has one angle of 110°, then:
\[
\text{Sum of the other two angles} = 180° - 110° = 70°
\]
But since only one angle is given, we cannot determine the exact values of the other two angles without additional information. Assuming the question meant to provide more details, let's move to the next part.
If we assume the triangle has one angle of 40° (as shown in the image), then:
\[
\text{Missing angle} = 180° - (40° + 110°) = 180° - 150° = 30°
\]
Answer for part (b):
\[
\boxed{30°}
\]
---
c)
The given angles are:
- One angle = 62°
- Another angle = 75°
To find the missing angle:
\[
\text{Missing angle} = 180° - (62° + 75°) = 180° - 137° = 43°
\]
Answer for part (c):
\[
\boxed{43°}
\]
---
d)
The given angles are:
- One angle = 90° (right angle)
- Another angle = 51°
To find the missing angle:
\[
\text{Missing angle} = 180° - (90° + 51°) = 180° - 141° = 39°
\]
Answer for part (d):
\[
\boxed{39°}
\]
---
e)
The given angles are:
- One angle = 46°
- Another angle = 59°
To find the missing angle:
\[
\text{Missing angle} = 180° - (46° + 59°) = 180° - 105° = 75°
\]
Answer for part (e):
\[
\boxed{75°}
\]
---
f)
The given angles are:
- One angle = 37°
- Another angle = 85°
To find the missing angle:
\[
\text{Missing angle} = 180° - (37° + 85°) = 180° - 122° = 58°
\]
Answer for part (f):
\[
\boxed{58°}
\]
---
Final Answers:
\[
\boxed{50°, 30°, 43°, 39°, 75°, 58°}
\]
Parent Tip: Review the logic above to help your child master the concept of finding missing angles in a triangle worksheet.
