Question

Complete.

If $m\angle 6=x$, $m\angle 7=x-20$and $m\angle 11=80$then $x=?$

Short answer

If $m\angle 6=x,m\angle 7=x-20$ and $m\angle 11=80$ then the value of x is b.

Step-by-step solution

Step 1. Observe the given figure and highlight angle 6, angle 7 and angle 11.

Step 2. Apply exterior angle theorem.

The measure of an exterior angle of a triangle is equal to the sum measures of two remote interior angles of a triangle.

Step 3. Description of step.

From the given figure, it can be observed that $\angle 11$is exterior angle and $\angle 6$and $\angle 7$are remote interior angles. Therefore, the sum of measures of $\angle 6$and $\angle 7$is equal to measure of $\angle 11$, that is,

$$\begin{gathered} m\angle 6+m\angle 7=m\angle 11 \\ x+x-20=80 \\ 2x=100 \end{gathered}$$

Step 4. Description of step.

Divide each side of the equation obtained in step 3 by 2 to find the value of x.

$\begin{array}{c}\frac{2x}{2}=\frac{100}{2}\\ x=50\end{array}$

Therefore, the value of x is 50.