Find the measure of ∠C if
∠A = 3 2 x + 20
∠B = 7 2 x + 20
∠C = 5 2 x + 40
∠D = 3 2 x + 10
\((32x+20) + (72x+20) + (52x+40) + (32x+10)=180 \\ 32x+72x+52x+32x +20+20+40+10 =180 \\ 188x+90=180 \\ -90 \\ 188x=90 \\ /188 \\ x=0.478\)
then \(52(0.478)+40 \\ 24.856+40=64.856\)
∠C = 64.856
Answer:
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°