Question

Find measure B ???????

Answer 1

The place to start is with this fact: the sum (total) of all the angles of a quadrilateral is 360 degrees. You know the two right angles (90 degrees each), so

90 + 90 + (7x + 27) + (9x - 7) = 360

Simplify and solve.

180 + 16x + 20 = 360
16x + 20 = 180
16x = 160
x = 10

Now plug this in for x in the two "algebra" angle measures.

Answer 2

The interior angles in a 4 sided polygon add up to 360°. You are already given two measurements of 90°, so you know that the lastvtwo angles sum to 360-90-90= 180°.
Put this information into an equation and solve for x:
(7x+27)°+(9x-7)°=180°
7x+27°+9x-7°=180°
16x+20°=180°
16x=160°
x=10°
Angle B is (7x+27)°, so just substitute x:
B = 7(10)+27
B = 70+27
B = 97°