Question

Find the measure of ∠C if

Answer 1

$(32x+20) + (72x+20) + (52x+40) + (32x+10)=180 \\ 32x+72x+52x+32x +20+20+40+10 =180 \\ 188x+90=180 \\ -90 \\ 188x=90 \\ /188 \\ x=0.478$
then $52(0.478)+40 \\ 24.856+40=64.856$
∠C = 64.856

Answer 2

Answer:

The measure of angle C is 114.672°

Step-by-step explanation:

Given: Measure of angles as

 ∠A = 32x + 20

∠B = 72x + 20

∠C = 52x + 40

∠D = 32x + 10

we have to find the measure of angle C.

Consider the given angles.

Since, there are four angles, so the figure must be a quadrilateral.

Also, we know,

Sum of measure of angles of a quadrilateral is 360°

Thus,  ∠A  + ∠B + ∠C +  ∠D = 360°

Substitute  the values , we get,

32x + 20 + 72x + 20 + 52x + 40 + 32x + 10 =360

188x + 90 = 360  

188x = 270

$x=\frac{270}{188}=1.436$

Thus, Measure of angle C is   52(1.436) + 40 =114.672

Thus, The measure of angle C is 114.672°