If PQRS is a kite, find m angle Q

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°

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