Question

In the figure shown below, the measure of $\angle BAC$ is ${(x+20)}^o$ and the measure of $\angle BAD$ is ${90}^o$. What is the measure of $\angle CAD$?

• A. ${(x-70)}^o$
• B. ${(70-x)}^o$
• C. ${(70+x)}^o$
• D. ${(160-x)}^o$
• E. ${(160+x)}^o$

Answer 1

Answer: (B)

${(70-x)}^o$

Given, $\angle BAC=(x+{20}^0)$ and $\angle BAD={90}^0$

From the given figure, we have

$\angle BAD=\angle BAC+\angle CAD\Rightarrow {90}^0=(x+{20}^0)+\angle CAD\Rightarrow \angle CAD={(70-x)}^0$