Given δrst congruent to δnpq, m∠r = -7x + 9, m∠n = -10x, find m∠r and m∠n.

 m∠R=30° m∠N=30°

If ΔRST is congruent to ΔNPQ, then we can infer that m∠R is congruent to m∠N

m∠R=-7x+9

m∠N=-10x

If both angles are congruent, we can solve for x...

-7x+9=-10x
add 7x to both sides
9=-3x
divide both sides by -3
-3=x

Now that we know the value of x, we can solve for the measure of the angles.

m∠R=-7x+9
m∠R=-7(-3)+9
m∠R=21+9
m∠R=30°

m∠N=-10x
m∠N=-10(-3)
m∠N=30°