Question

Solve. Justify your responses. a Given:a║b and c║d, m∠ 4=35° Find: m∠1, m∠2, and m∠3

Answer 1

m∠1 = 90°

m∠2 = 35°

m∠3 = 55°

Explanation:

Find the diagram attached

From the diagram:

`m<3+m<4=90 (complementary \ angles)\\`

Given that <4 = 35°

`m<3 = 90 - m<4\\m<3=90-35\\m<3=55^0`

The sum of the angle on a straight line at point A is 180°. Hence:

`90+m<1 =180\\\m<1 = 180 - 90\\m<1=90^0`

The sum of angle in the triangle ABC is 180°, hence;

`m<1+m<2+m<3=180\\90+m<2+55=180\\m<2+145=180\\m<2=180-145\\m<2=35^0`