Q14. - Geometry

Question

1. $m\angle CBD=\_\_\_\_\_$
   
2. Name the postulate that justifies your answer in part (a).

Step-by-Step Solution

Answer

1. The blank space should be filled with $92°$.
2. The satisfying postulate is postulate 4.

Part a. Step 1. Observe the figure.

The provided figure represents two equal angles which are $\angle ABD$ and $\angle CBD$ which are the parts of angle $\angle AOC$. The value of angle $\angle ABD$ is represented by $88°$.

Part a. Step 2. Use the observation.

As the $\angle AOC$ represents itself as a straight angle so the addition of both the angles $\angle ABD$ and $\angle CBD$ will be equal to $180°$.

Part a. Step 3. Determine the value of given angle.

Make an equation by taking the addition of the angles $\angle ABD$ and $\angle CBD$ equal to $180°$.

$$\begin{gathered} m\angle CBD+m\angle ABD=180° \\ m\angle CBD+88°=180° \\ m\angle CBD=180°-88° \\ m\angle CBD=92° \end{gathered}$$

Part b. Step 1. Observe the figure.

The provided figure represents two equal angles which are $\angle ABD$ and $\angle CBD$ which are the parts of angle $\angle AOC$. The value of angle $\angle ABD$ is represented by $88°$.

Part b. Step 2. Use the observation.

As the $\angle AOC$ represents itself as a straight angle so the addition of both the angles $\angle ABD$ and $\angle CBD$ will be equal to $180°$.

Part b. Step 3. Determine the postulate.

The postulate 4 satisfies the answer of part (a) because postulate 4 states that if an angle represents itself as a straight angle so the addition of angles that are present in that angle will be equal to $180°$.