Question

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

Answer 1

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Answer 2

Answer:

m∠3=115°.

Step-by-step 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°.