Question

∠1 and ∠2 create a linear pair of angles. if the measure of ∠1 is four times the measure of ∠2, what is the measure of ∠1? select one answer a 18° b 36° c 72° d 144°

Explanation:

Step1: Recall linear pair property

A linear pair of angles sums to \(180^\circ\). Let \(m\angle2 = x\), then \(m\angle1 = 4x\).

Step2: Set up equation

Since \(\angle1\) and \(\angle2\) are a linear pair, \(m\angle1 + m\angle2 = 180^\circ\). Substitute the expressions: \(4x + x = 180^\circ\).

Step3: Solve for \(x\)

Combine like terms: \(5x = 180^\circ\). Divide both sides by 5: \(x=\frac{180^\circ}{5}=36^\circ\).

Step4: Find \(m\angle1\)

Since \(m\angle1 = 4x\), substitute \(x = 36^\circ\): \(m\angle1 = 4\times36^\circ = 144^\circ\).

Answer:

D. \(144^\circ\)