Question

Find the measure of ∠A if ∠A = 3 2 x + 20 ∠B = 7 2 x + 20 ∠C = 5 2 x + 40 ∠D = 3 2 x + 10

Answer 1

65°

Explanation:

Opposite angles in a cyclic quadrilateral are supplementary.

5

2

x + 40 +

3

2

x + 20 = 180

x = 30

then,

∠A =

3

2

x + 20

∠A =

3

2

(30) + 20 = 65

Answer 2

The measure of all the internal angles need to measure 360. How you do this question is you add all the angle measurements and then equal them to 360. Find x and to find the measure of angle A you just insert the measure of x in the problem.
32x+20+72x+20+32x+10+52x+40=360 (add)
188x+90=360 (subtract 90 from both sides)
188x=270 (divide both sides by 188)
x=1.4
32(1.4)+20=66 (rounded)