Given m∠2 = 80°, m∠1 = 4 · m∠3, and ∠4 ≅ ∠ 8, find m∠1, m∠3, m∠4, m∠5, m∠6, m∠7, and m∠8.

m∠1 = m∠5 = 100°, m∠2 = m∠6 = 80°, m∠4=m∠8 = 155°, m∠3 = m∠7 = 25°

Step-by-step explanation:

Supposing ∠1,∠2 make up a straight angle. Let ∠1, ∠5 and ∠2 and ∠6 be corresponding angles on a transversal drawn on two parallel lines. ∠3,∠4 and∠5 ∠6 be interior angles

If m ∠ = 80° them m∠ 1 = 100°

As ∠1 = 4. m∠3 therefore

100° = 4. m∠3

m∠3 = 100/4 = 25°

Again supposing m∠3 + m∠4 = 180°

m∠4 = 180° - 25° = 155°

m∠4 = m∠8 = 155°

m∠8 + m∠7 = 180°

m∠7 = 180° - 155° = 25°

Let ∠5 and ∠1 be corresponding angles so m∠5 = m∠1 = 100°

and m∠6 = m∠2 = 80°