Question

Find the measure of <_B. Show your work!

Answer 1

Answer: 51

Step-by-step explanation:

So angle C of the triangle and the 111 degree angles next to each other are supplementary angles, so they must add up to 180.

so 111 + C = 180

C = 69 degrees

In a triangle, all three angles must add up to 180

so A + B + C = 180

we already found the value of angle C, and the equations 4y and 3y + 6 are given for angles A and B respectively, so plugging in values we get

(4y) + (3y + 6) + (69) = 180 combine like terms

7y + 75 = 180 and solve for y

7y = 105

y = 15

now that we have the value of y, we can plug it back into B = 3y + 6 to get

B = 3y + 6

B = 3(15) + 6

= 45 + 6

= 51