Question

Given m 1= 65, find the measure of each missing angle.Givd your reasoning

Answer 1

Answer:

Step-by-step explanation:

Given:

m∠1 = 65°

Since. ∠1 and ∠2 are the angles of linear pair,

m∠1 + m∠2 = 180°

65° + m∠2 = 180°

m∠2 = 115°

m∠1 = m∠3 [Vertical angles]

m∠3 = 115°

Since, ∠1 and ∠4 is the linear pair of angles,

m∠1 + m∠4 = 180°

65° + m∠4 = 180°

m∠4 = 180 - 65 = 115°

m∠4 + m∠5 = 180° [Consecutive interior angles between the parallel lines]

115° + m∠5 = 180°

m∠5 = 180° - 115° = 65°

m∠5 + m∠6 = 180° [Linear pair of angles]

65° + m∠6 = 180°

m∠6 = 115°

m∠5 = m∠7 [Vertical angles]

m∠5 = m∠7 = 65°

m∠6 = m∠8 [Vertical angles]

m∠6 = m∠8 = 115°