Question

fill in the blank 4 points. if ∠1 and ∠2 are congruent and supplementary angles, how much does each angle measure? m∠1 = type your answer... degrees m∠2 = type your answer... degrees

Explanation:

Step1: Recall definitions

Congruent angles have equal measures, and supplementary angles add up to 180 degrees. Let \(m\angle1 = x\) and \(m\angle2=x\) (since they are congruent).

Step2: Set up equation

We know that \(m\angle1 + m\angle2=180^{\circ}\), substituting \(m\angle1 = x\) and \(m\angle2 = x\) gives \(x + x=180^{\circ}\), or \(2x = 180^{\circ}\).

Step3: Solve for \(x\)

Dividing both sides of the equation \(2x = 180^{\circ}\) by 2, we get \(x=\frac{180^{\circ}}{2}=90^{\circ}\). So \(m\angle1 = 90^{\circ}\) and \(m\angle2 = 90^{\circ}\).

Answer:

\(m\angle1 = 90\), \(m\angle2 = 90\)