Q20 - Geometry

Question

Complete. $m\angle 6+m\angle 5=m\angle ?$

Step-by-Step Solution

Answer

The answer is $m\angle 6+m\angle 5=\mathbf{180}\mathbf{°}\mathbf{-}\mathit{m}\mathbf{\angle }\mathbf{7}$

Step 1. Apply the definition of sum of angles on a straight line.

The sum of all angles on a straight line is $180°$.

Step 2. Description of step.

Since, angles on straight line ADE are $m\angle 5$, $m\angle 6$, and $m\angle 7$, therefore,  $m\angle 5+m\angle 6+m\angle 7=180°$.

Step 3. Calculate m∠7+m∠6=m∠?

In order to find $m\angle 6+m\angle 5$, subtract $m\angle 7$ from both sides of the equation $m\angle 5+m\angle 6+m\angle 7=180°$.

$\begin{array}{l} m\angle 5+m\angle 6+m\angle 7=180°\\ m\angle 5+m\angle 6+m\angle 7-m\angle 7=180°-m\angle 7\\ m\angle 6+m\angle 5=180°-m\angle 7\end{array}$

Therefore, $m\angle 6+m\angle 5=180°-m\angle 7$.