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
[tex]m\ BAD+127^o=180^o[/tex] ----> by supplementary angles (form a linear pair)
[tex]m\ BAD=180^o-127^o=53^o[/tex]
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
[tex]m\ BAD+m\ ADB+m\ ABD=180^o[/tex]
we have
[tex]m\ BAD=53^o[/tex]
[tex]m\ ADB=90^o[/tex]
substitute
[tex]53^o+90^o+m\ ABD=180^o[/tex]
[tex]143^o+m\ ABD=180^o[/tex]
[tex]m\ ABD=180^o-143^o[/tex]
[tex]m\ ABD=37^o[/tex]
step 3
Find the measure of angle w
we know that
[tex]m\ ABD+w=180^o[/tex] ----> by supplementary angles (form a linear pair)
we have
[tex]m\ ABD=37^o[/tex]
substitute
[tex]37^o+w=180^o[/tex]
[tex]w=180^o-37^o[/tex]
[tex]w=143^o[/tex]
step 4
Find the measure of angle r
we have
[tex]r=2w[/tex] ----> given problem
substitute the value of w
[tex]r=2(143^o)=286^o[/tex]
