Question

Please help me 10 points

Answer 1

Let us prove that angle 1 is complementary to angle 3 step by step.

1. We have been given that angle 1 is complementary to angle 2.

2. Since we know that complementary angles add up to 90 degrees, therefore, by the definition of complementary $m\angle 1+ m\angle 2=90^{o}$.

3. We have been also given that line segment  BD bisects $\angle ADC$.                

4. By the definition of bisect $\angle 2 \cong \angle 3$.

5. Angles are congruent if their measures, in degrees, are equal, therefore, by angle congruence postulate  $m\angle 2=m\angle 3$.        

6. $m\angle 1+ m\angle 2=90^{o}$

Upon substituting $m\angle 2=m\angle 3$ in above equation we will get,

$m\angle 1+ m\angle 3=90^{o}$  

Therefore, by substitution property of equality $m\angle 1+ m\angle 3=90^{o}$ .

Hence, proven that angle 1 is complementary to angle 3.