The following are the measures of the angles;
1. m∠4 = 81°
2. m∠1 = m∠2 = 55°
What are the measures of the angles?
m∠1 = 42°
m∠2 = 39°
m∠1 + m∠2 + m∠3 = 180° (sum of angles in a triangle)
42° + 39° + m∠3 = 180°
81 + m∠3 = 180°
m∠3 = 180 - 81
m∠3 = 99°
So,
m∠3 + m∠4 = 180°
99° + m∠4 = 180°
m∠4 = 180° - 99°
m∠4 = 81°
m∠4 = 110°
m∠3 + m∠4 = 180° (supplementary angles)
m∠3 + 110 = 180
m∠3 = 180 - 110
m∠3 = 70°
So,
m∠1 + m∠2 + m∠3 = 180° (sum of angles in a triangle)
m∠1 = m∠2
So,
2(m∠1) + m∠3 = 180°
2(m∠1) + 70° = 180°
2(m∠1) = 180 - 70
2(m∠1) = 110°
Divide both sides by 2
m∠1 = 110°/2
m∠1 = 55°
Therefore, m∠1 = m∠2 = 55°