Answer:
m<Q = 78°
Step-by-step explanation:
First, find the value of x:
7x + 2 = 10x - 31 (Non-vertex angles of a kite are congruent to each other)
Collect like terms
7x - 10x = -2 - 31
-3x = -33
Divide both sides by -3
x = 11
Find m<Q:
Sum of all angles in a kite = 360°
Therefore,
m<Q + m<P + m<S + m<R = 360°
m<Q + (7x + 2) + 124 + (10x - 31) = 360
Plug in the value of x
m<Q + (7*11 + 2) + 124 + (10*11 - 31) = 360
m<Q + 79 + 124 + 79 = 360
m<Q + 282 = 360
Subtract 282 from both sides
m<Q + 282 - 282 = 360 - 282
m<Q = 78°
