Question 56

In the given figure, if AC, DE are parallel and $$\angle$$CAB = 38$$^\circ$$, then the value of $$\angle$$ABC + 5$$\angle$$CBD is:

Solution

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


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