Chapter E, Problem 3.12EX

To determine

To find the value of x.

Answer to Problem 3.12EX

Option (a) $41$ is correct.

Explanation of Solution

Given information: A, B, C, and D are coplanar points. $\overleftrightarrow{AB}\parallel \overleftrightarrow{CD}$ , $\overleftrightarrow{AB}\perp \overleftrightarrow{AC}$ and $m\angle ACD=2x+8$ .

Options,

a. $41$

b. $49$

c. $90$

d. $180$

Calculation: The required solutions is obtained as,

Give that $\overleftrightarrow{AB}\parallel \overleftrightarrow{CD}$ , $\overleftrightarrow{AB}\perp \overleftrightarrow{AC}$

Since they are coplanar, AC is a transversal line. Thus $\angle CAD$ and $\angle ACD$ are interior angles.

Using theorem they are supplementary to each other.

  $\begin{array}{l}\angle CAD+\angle ACD=180\\ 90+2x+8=180\\ 2x=82\\ x=41\end{array}$

Therefore, option (a) $41$ is correct.