To solve the missing angles in the given triangles, we use the fundamental property of triangles:
the sum of the interior angles of a triangle is always 180°. Let's solve each problem step by step.
---
Problem 1
Given angles: \(132^\circ\) and \(21^\circ\)
The sum of the angles in a triangle is \(180^\circ\):
\[
x + 132^\circ + 21^\circ = 180^\circ
\]
Simplify:
\[
x + 153^\circ = 180^\circ
\]
Solve for \(x\):
\[
x = 180^\circ - 153^\circ = 27^\circ
\]
Answer for Problem 1:
\[
x = 27^\circ
\]
---
Problem 2
Given angles: \(7^\circ\) and \(131^\circ\)
The sum of the angles in a triangle is \(180^\circ\):
\[
x + 7^\circ + 131^\circ = 180^\circ
\]
Simplify:
\[
x + 138^\circ = 180^\circ
\]
Solve for \(x\):
\[
x = 180^\circ - 138^\circ = 42^\circ
\]
Answer for Problem 2:
\[
x = 42^\circ
\]
---
Problem 3
Given angles: \(100^\circ\) and \(28^\circ\)
The sum of the angles in a triangle is \(180^\circ\):
\[
x + 100^\circ + 28^\circ = 180^\circ
\]
Simplify:
\[
x + 128^\circ = 180^\circ
\]
Solve for \(x\):
\[
x = 180^\circ - 128^\circ = 52^\circ
\]
Answer for Problem 3:
\[
x = 52^\circ
\]
---
Problem 4
Given angles: \(31^\circ\) and \(119^\circ\)
The sum of the angles in a triangle is \(180^\circ\):
\[
x + 31^\circ + 119^\circ = 180^\circ
\]
Simplify:
\[
x + 150^\circ = 180^\circ
\]
Solve for \(x\):
\[
x = 180^\circ - 150^\circ = 30^\circ
\]
Answer for Problem 4:
\[
x = 30^\circ
\]
---
Problem 5
Given angles: \(31^\circ\) and \(90^\circ\) (right angle)
The sum of the angles in a triangle is \(180^\circ\):
\[
x + 31^\circ + 90^\circ = 180^\circ
\]
Simplify:
\[
x + 121^\circ = 180^\circ
\]
Solve for \(x\):
\[
x = 180^\circ - 121^\circ = 59^\circ
\]
Answer for Problem 5:
\[
x = 59^\circ
\]
---
Problem 6
Given angles: \(41^\circ\) and \(67^\circ\)
The sum of the angles in a triangle is \(180^\circ\):
\[
x + 41^\circ + 67^\circ = 180^\circ
\]
Simplify:
\[
x + 108^\circ = 180^\circ
\]
Solve for \(x\):
\[
x = 180^\circ - 108^\circ = 72^\circ
\]
Answer for Problem 6:
\[
x = 72^\circ
\]
---
Problem 7
Given angles: \(56^\circ\) and \(44^\circ\)
The sum of the angles in a triangle is \(180^\circ\):
\[
x + 56^\circ + 44^\circ = 180^\circ
\]
Simplify:
\[
x + 100^\circ = 180^\circ
\]
Solve for \(x\):
\[
x = 180^\circ - 100^\circ = 80^\circ
\]
Answer for Problem 7:
\[
x = 80^\circ
\]
---
Problem 8
Given angles: \(60^\circ\) and \(60^\circ\)
The sum of the angles in a triangle is \(180^\circ\):
\[
x + 60^\circ + 60^\circ = 180^\circ
\]
Simplify:
\[
x + 120^\circ = 180^\circ
\]
Solve for \(x\):
\[
x = 180^\circ - 120^\circ = 60^\circ
\]
Answer for Problem 8:
\[
x = 60^\circ
\]
---
Final Answers:
\[
\boxed{27^\circ, 42^\circ, 52^\circ, 30^\circ, 59^\circ, 72^\circ, 80^\circ, 60^\circ}
\]
Parent Tip: Review the logic above to help your child master the concept of triangle interior angles worksheet.
