Question

Angle r° = 2w°. What is the measure of angle r°?

Answer 1

Answer:

Option B. 286 degrees

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

Find the measure of angle BAD in triangle A

$m\ BAD+127^o=180^o$ ----> by supplementary angles (form a linear pair)

$m\ BAD=180^o-127^o=53^o$

step 2

Find the measure of angle ABD in triangle A

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

$m\ BAD+m\ ADB+m\ ABD=180^o$

we have

$m\ BAD=53^o$

$m\ ADB=90^o$

substitute

$53^o+90^o+m\ ABD=180^o$

$143^o+m\ ABD=180^o$

$m\ ABD=180^o-143^o$

$m\ ABD=37^o$

step 3

Find the measure of angle w

we know that

$m\ ABD+w=180^o$ ----> by supplementary angles (form a linear pair)

we have

$m\ ABD=37^o$

substitute

$37^o+w=180^o$

$w=180^o-37^o$

$w=143^o$

step 4

Find the measure of angle r

we have

$r=2w$ ----> given problem

substitute the value of w

$r=2(143^o)=286^o$