Question

3 given: ∠1 and ∠2 form a right angle; m∠1 + m∠3 = 90° prove: ∠2 ≅ ∠3 statements reasons 1. ∠1 and ∠2 form a right angle 1. 2. ∠1 and ∠2 are complementary 2. 3. m∠1 + m∠3 = 90° 3. 4. ∠1 and ∠3 are complementary 4. 5. ∠2 ≅ ∠3 5.

Explanation:

Step1: Given information

Given

Step2: Definition of complementary angles

If two angles form a right - angle, they are complementary.

Step3: Given information

Given

Step4: Definition of complementary angles

If the sum of two angles is 90°, they are complementary.

Step5: Congruence of complementary angles

If two angles are complementary to the same angle, they are congruent.

Answer:

Statements	Reasons
2. $\angle1$ and $\angle2$ are complementary	2. Definition of complementary angles (if two angles form a right - angle, they are complementary)
3. $m\angle1 + m\angle3=90^{\circ}$	3. Given
4. $\angle1$ and $\angle3$ are complementary	4. Definition of complementary angles (if the sum of two angles is 90°, they are complementary)
5. $\angle2\cong\angle3$	5. If two angles are complementary to the same angle, they are congruent