in triangle PQR ~ -- ~ -- if m<P
= PQ = QR.
4x + 50, m<Q =2x + 60 and m<R = 14x + 30, find the measure of each angle.
To find the measure of each angle in triangle PQR, we need to determine the numerical values of m<P, m<Q, and m<R.
Given that P and Q are congruent, we can equate their measures:
m<P = m<Q
4x + 50 = 2x + 60
Simplifying the equation:
4x - 2x = 60 - 50
2x = 10
x = 5
Now we can substitute the value of x back into the equations to find the measures of each angle:
m<P = 4x + 50
m<P = 4(5) + 50
m<P = 20 + 50
m<P = 70
m<Q = 2x + 60
m<Q = 2(5) + 60
m<Q = 10 + 60
m<Q = 70
m<R = 14x + 30
m<R = 14(5) + 30
m<R = 70 + 30
m<R = 100
Therefore, the measures of each angle are:
m<P = 70 degrees
m<Q = 70 degrees
m<R = 100 degrees.