Question

In figure, $ \angle \mathrm{BAC}=90°$, $ \mathrm{AD}\perp \mathrm{BC}$ and $ \angle \mathrm{BAD}=50°$, then $ \angle \mathrm{ACD}$ is

O

• A. $50°$
• B. $40°$
• C. $70°$
• D. $60°$

Answer 1

The correct option is A

$50°$

The explanation for the correct answer.

Find the required angle:

Given: $\angle \mathrm{BAC}=90°$ and $\angle \mathrm{BAD}=50°$

Therefore,

$$\begin{gathered} \angle \mathrm{DAC}=\angle \mathrm{BAC}-\angle \mathrm{BAD} \\ \angle \mathrm{DAC}=90°-50° \\ \angle \mathrm{DAC}=40° \end{gathered}$$

Now in triangle $\mathrm{ADC}$,

$\angle \mathrm{ACD}+\angle \mathrm{DAC}+\angle \mathrm{ADC}=180°$ (Sum angle property of triangle)

$$\begin{gathered} \Rightarrow \angle \mathrm{ACD}+40°+90°=180 \\ \Rightarrow \angle \mathrm{ACD}+130°=180° \\ \Rightarrow \angle \mathrm{ACD}=180°-130° \\ \Rightarrow \angle \mathrm{ACD}=50° \end{gathered}$$

Hence option $A$ is correct.