Question

For questions 13 – 15, find x so that q || r. State the converse used.

Answer 1

Answer:

13. x = 7 ; Converse : Alternate interior angles are equal .

14.  x=12; Converse used : Linear pair

15.  x = 23; Converse: Corresponding angles are equal

Step-by-step explanation:

13.

Refer the attached figure

Given: q || r

$\angle CBE =\angle DEB$ (Alternate interior angles )

So,  15x+3=108

15x=108-3

15x=105

$x=\frac{105}{15}$

x=7

So, x = 7 ; Converse : Alternate interior angles are equal .

14.

Refer the attached figure

Given q||r

$\angle PQT = \angle STQ$ (Alternate interior angles

So,$\angle PQT = \angle STQ=11x-28$

Now$\angle UTQ + \angle STQ = 180^{\circ}$(Linear pair)

So,7x-8+11x-28=180

18x-36= 180

18x=216

$x=\frac{216}{18}$

x=12

So, x=12; Converse used : Linear pair

15.

Refer the attached figure

Given q||r

$\angle BDC+\angle CDE = 90+2x$

$\angle BDE=\angle PBC$(corresponding angles)

90+2x=5x+21

90-21=5x-2x

69=3x

23=x

So, x = 23; Converse: Corresponding angles are equal