Question

Find the measure of $\angle$2, $\angle$3 and $\angle$4 from the given figure.

• A. 75${}^{\circ }$, 75${}^{\circ }$, 105${}^{\circ }$
• B. 75${}^{\circ }$, 85${}^{\circ }$, 105${}^{\circ }$
• C. 105${}^{\circ }$, 75${}^{\circ }$, 75${}^{\circ }$
• D. 105${}^{\circ }$, 75${}^{\circ }$, 105${}^{\circ }$

Answer 1

The correct option is D

105${}^{\circ }$, 75${}^{\circ }$, 105${}^{\circ }$

From the figure given in the question, we can observe that

$\angle$3 = 75${}^{\circ }$
(Vertically opposite angles)

$\angle$2 +75${}^{\circ }$ = 180${}^{\circ }$
(Angles on a straight line)

$\Rightarrow$ $\angle$2 = 180${}^{\circ }$- 75${}^{\circ }$ = 105${}^{\circ }$

$\angle$2 = $\angle$4
(Vertically opposite angles)

$\Rightarrow$$\angle 4$ = 105°