Chapter 2.7, Problem 12PSB

To determine

To prove : The congruency of $\angle A\cong \angle C$ is to be proved

Explanation of Solution

Given information : The following information has been given

  $\angle A$ is complementary to $\angle ADB$

  $\angle C$ is complementary to $\angle CDB$

  $\overrightarrow{DB}$ bisects $\angle ADC$

Formula used : If two angles have same complementary angles, then the two angles are said to be congruent

Proof : If $\overrightarrow{DB}$ bisects $\angle ADC$ , then we can say that

  $\angle ADB=\angle CDB$

Now, if $\angle A$ is complementary to $\angle ADB$ , then we can also say that $\angle A$ is complementary to $\angle CDB$

But we know that $\angle C$ is complementary to $\angle CDB$

Hence, we can say that $\angle A\cong \angle C$

Thus, the required angles are proved