Question

given
∠x and ∠y are supplementary
∠x ≅ ∠y
∠z is a right angle
prove
∠x ≅ ∠z
statement

1. ∠x and ∠y are supplementary
2. ∠x ≅ ∠y
3. ∠x and ∠y are right angles
4. ∠z is a right angle
5. ∠x ≅ ∠z

reason

1. given
2. given
3. ?
4. given
5. congruent right angles theorem

Explanation:

Step1: Recall the definition of supplementary angles

If two angles are supplementary, their sum is \(180^{\circ}\). Let \(\angle X=\angle Y = x\). Then \(x + x=180^{\circ}\), so \(2x = 180^{\circ}\).

Step2: Solve for \(x\)

Divide both sides of the equation \(2x = 180^{\circ}\) by \(2\). We get \(x=\frac{180^{\circ}}{2}=90^{\circ}\). This is based on the theorem that if two congruent angles are supplementary, then each angle is a right angle.

Answer:

If two congruent angles are supplementary, then each angle is a right angle.