Question

M∠6 is (2x – 5)° and m∠8 is (x + 5)°. What is m∠3?

Answer 1

I hope this helps you

Answer 2

m∠3=115°.

Explanation:

It is given from the figure that line q is parallel to s and r is the transversal.

Since, m∠6 and m∠8 forms a linear pair as they are on the straight line r, therefore using the linear pair property, we have

m∠6+m∠8=180°

⇒
`2x-5+x+5=180^(\circ)`

⇒
`3x=180^(\circ)`

⇒
`x=60^(\circ)`

Thus, the measure of ∠6 is
`2x-5=2(60)-5=120-5=115^(\circ)`

Now, m∠3=m∠6=115° as both m∠3 and m∠6 forms the alternate interior angle pair.

Therefore, the measure of m∠3=115°.