Question

9. In the diagram below, a Il b. Use the following information to find

and write the missing angle measures onto the diagram.

Answer 1

For angles on the transversal line d:

m∠1 = m∠2 = m∠4 = m∠6 = 148°

m∠3 = m∠5 = 32°

For angles on the transversal line c:

m∠7 = m∠9 = m∠10 = 100°

m∠8 = m∠11 = m∠12 = 80°

When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, and alternate angles.

For angles on the transversal line d we have that;

8x - 8 = 3x + 17 {vertical angles are equal}

8x - 3x = 17 + 8

5x = 25

x = 5

8(5) - 8 = 32 so;

32 + m∠1 = 180° {straight line angles}

m∠1 = 180 - 32

m∠1 = 148°

m∠1 = m∠2 = 148° {vertical angles are equal}

m∠3 = m∠5 and m∠4 = m∠6 {corresponding}

m∠3 = 32°

m∠4 = m∠5 = 148°

For angles on the transversal line c we have that;

4y + 44 + 6y + 46 = 180° {alternate exterior angles}

10y + 90 = 180

10y = 180 - 90

10y = 90

y = 9

4(9) + 44 = 80° so;

m∠8 = 80° {vertical angles}

80 + m∠7 = 180

m∠7 = 180 - 80

m∠7 = 100°

m∠7 = m∠9 = m∠10 = 100° {corresponding angles}

m∠8 = m∠11 = m∠12 = 80° {corresponding angles}

Therefore, for angles on the transversal line d, m∠1 = m∠2 = m∠4 = m∠6 = 148° and m∠3 = m∠5 = 32°. For the angles on the transversal line c, m∠7 = m∠9 = m∠10 = 100° and m∠8 = m∠11 = m∠12 = 80°.