Question

what is the value of m?
○ 10
○ 30
○ 70
○ 150
$(5m + 100)^circ$
$(2m + 10)^circ$

Explanation:

Step1: Identify supplementary angles

The two angles are same-side interior angles formed by parallel lines cut by a transversal, so they are supplementary (sum to $180^\circ$).
$$(5m + 100) + (2m + 10) = 180$$

Step2: Combine like terms

Add the variable terms and constant terms together.
$$7m + 110 = 180$$

Step3: Isolate the variable term

Subtract 110 from both sides of the equation.
$$7m = 180 - 110$$
$$7m = 70$$

Step4: Solve for m

Divide both sides by 7 to find the value of m.
$$m = \frac{70}{7}$$
$$m = 10$$

Answer:

10