Question

In $△$ ABC, BA is produced to E and AD = BD = AC; ∠CAE = 75^o and ∠ACD = x^o. Then, the value of x is

• A. 45°
• B. 50°
• C. 60°
• D. 37.5^o

Answer 1

The correct option is B

50°

In $△$ADC

$\angle$ADC = $\angle$ACD = x [angle opposite to equal sides in a triangle are equal.]

$\angle$ADB = ${180}^{\circ }$ – x [linear pair of angles]

In $△$ADB

$\angle$DAB = $\angle$DBA = y [angle opposite to equal sides in a triangle are equal.]

2y = x

$\angle$CAE = ${75}^{\circ }$ = x + $\frac{x}{2}$

x = ${50}^{\circ }$