Here, we are required to find the value of the other angles in the diagram attached to this answer sheet.
The value of the angles are;
- m∠1 = 82°
- m∠2 = 98°
- m∠3 = 23°
- m∠4 = 59°
- m∠5 = 121°
- m∠6 = 51°
- m∠7 = 59°
- m∠8 = 70°
- m∠9 = 51°
- m∠10 = 129°
The understanding of the triangle theorem and line theorems is very important to resolve this.
- The sum of angles in a triangle = 180⁰.
- The sum of angles on a straight line = 180⁰
- Alternate angles are equal.
m∠1 + m∠2 = 180° (Theorem: sum of angles on a straight line = 180⁰)
m∠1 + 98 = 180
m∠1 = 180 - 98
m∠2 + m∠3 + m∠7 = 180° (Theorem = sum of angles in a triangle = 180⁰)
98 + 23 + m∠7 = 180
m∠7 + 121 = 180
m∠7 = 180 - 121
m∠4 = m∠7 (Theorem = alternate angles are equal)
m∠6 + m∠7 + m∠8 = 180° (Theorem = sum of angles on a straight line = 180)
m∠6 + 59 + 70 = 180
m∠6 + 129 = 180
m∠6 = 180 - 129
m∠4 + m∠8 + m∠9 = 180° (Theorem = sum of angles in a triangle = 180)
59 + 70 + m∠9 = 180
m∠9 + 129 = 180
m∠9 = 180 - 129
m∠4 + m∠5 = 180° (Theorem = sum of angles on a straight line = 180)
m∠5 + 59 = 180
m∠5 = 180 - 59
m∠10 + m∠9 = 180° (Theorem = sum of angles on a straight line = 180⁰)
m∠10 + 51 = 180
m∠10 = 180 - 51
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