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°
What is the measure of the missing angles?
The sum of angles in a triangle = 180°.
The sum of angles on a straight line = 180°
Alternate angles are equal.
m∠1 + m∠2 = 180° (sum of angles on a straight line = 180°)
m∠1 + 98 = 180
m∠1 = 180 - 98
m∠1 = 82°
m∠2 + m∠3 + m∠7 = 180° (sum of angles in a triangle = 180°)
98 + 23 + m∠7 = 180
m∠7 + 121 = 180
m∠7 = 180 - 121
m∠7 = 59°
m∠4 = m∠7 (alternate angles are equal)
m∠4 = 59°
m∠6 + m∠7 + m∠8 = 180° (sum of angles on a straight line = 180°)
m∠6 + 59 + 70 = 180
m∠6 + 129 = 180
m∠6 = 180 - 129
m∠6 = 51°
m∠4 + m∠8 + m∠9 = 180° (sum of angles in a triangle = 180°)
59 + 70 + m∠9 = 180
m∠9 + 129 = 180
m∠9 = 180 - 129
m∠9 = 51°
m∠4 + m∠5 = 180° (sum of angles on a straight line = 180°)
m∠5 + 59 = 180
m∠5 = 180 - 59
m∠5 = 121°
m∠10 + m∠9 = 180° (sum of angles on a straight line = 180°)
m∠10 + 51 = 180
m∠10 = 180 - 51
m∠10 = 129°
Therefore, the missing angles are calculated using different angle theorem.