Sign in
Please select an account to continue using cracku.in
↓ →
In the given figure, if AC, DE are parallel and $$\angle$$CAB = 38$$^\circ$$, then the value of $$\angle$$ABC + 5$$\angle$$CBD is:
Given,
$$\angle$$CAB = 38$$^\circ$$
$$=$$> 2a = 38$$^\circ$$
$$=$$> a = 19$$^\circ$$
$$=$$> $$\angle$$CBD = 19$$^\circ$$
AB is the transversal intersecting parallel lines AC and DE
$$\therefore\ $$Alternate interior angles are equal
$$=$$> $$\angle$$ABE = $$\angle$$CAB
$$=$$> $$\angle$$ABE = 38$$^\circ$$
$$\angle$$ABE + $$\angle$$ABC + $$\angle$$CBD = 180$$^\circ$$
$$=$$> 38$$^\circ$$ + $$\angle$$ABC + 19$$^\circ$$ = 180$$^\circ$$
$$=$$> $$\angle$$ABC + 57$$^\circ$$ = 180$$^\circ$$
$$=$$> $$\angle$$ABC = 180$$^\circ$$ - 57$$^\circ$$
$$=$$> $$\angle$$ABC = 123$$^\circ$$
$$\therefore\ $$ $$\angle$$ABC + 5$$\angle$$CBD = 123$$^\circ$$ + $$5\left(19^{\circ\ }\right)$$ = 123$$^\circ$$ + 95$$^\circ$$ = 218$$^\circ$$
Hence, the correct answer is Option B
Create a FREE account and get: