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

a. 120 degrees
b. 286 degrees
c. 240 degrees
d. 143 degrees

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

----> by supplementary angles (form a linear pair)

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

we have

substitute

step 3

Find the measure of angle w

we know that

----> by supplementary angles (form a linear pair)

we have

substitute

step 4

Find the measure of angle r

we have

----> given problem

substitute the value of w

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle

I’ll you if you answer my questions!