Q3. - Geometry

Question

Given the diagram, tell whether you can reach the conclusion shown.

 

On $\angle AXC$ is a straight angle.

Step-by-Step Solution

Answer

The answer related to given sentence is yes.

Step 1. Determine which postulate is suitable.

Postulate 4 is the suitable postulate which 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 $180°$.

Step 2. Relate the given statement with the postulate.

Angle represents itself as a straight angle is $\angle AXC$ and the angle present in this angle are $\angle AXD$ and $\angle DXC$ so the addition of these angles will be equal to $180°$.

Step 3. Determine the answer by using the relation.

As the angle represents itself as a straight angle $\angle AXC$ and the angle present in this angle are $\angle AXD$ and $\angle DXC$ also the addition of these angles is equal to $180°$ so the value of $\angle AXC$ is also $180°$ because the addition of $\angle AXD$ and $\angle DXC$ is equal to $\angle AXC$.