If m ∥ n, m∠1 = (5x + 12)°, and m∠2 = (7x – 16)°, what is m∠3?

98°

Step-by-step explanation:

m∠1 = m∠2

5x + 12 = 7x - 16; substitute the given

2x = 28

x = 14

m∠2 + m∠3 = 180; supplementary angles

82 + m∠3 = 180

m∠3 = 180 - 82

m∠3 = 98 degrees

m<3 = 98

Explanation: If two parallel lines are cut by a transversal,

then alternate interior angles are congruent.

This means that the m<1 = m<2.

So we can setup the equation 5x + 12 = 7x - 16

and solving this equation gives us x = 14.

Now let's use <2 to help us find the m<3.

Since x = 14, we can plug a 14 into the equation for x

to find the m<2 and this gives us 7(14) - 16 which is 82.

Now, we know that <2 and <3 form a straight

angle which is equal to 180 degrees.

So we can say that 82 + m<3 = 180 and we find that m<3 = 98.