Question

From the figure given below, find out the measure of $\angle$ABD and $\angle$DBC respectively.

• A. 24 and 126
• B. 42 and 156
• C. 24 and 156
• D. 42 and 126

Answer 1

The correct option is C

24 and 156

Since ABC is a straight line, $\angle$ABC = $\angle$ABD + $\angle$DBC

And also, since ABC is a straight line, $\angle$ABC=180${}^{\circ }$

$\therefore$ $\angle$ABD + $\angle$DBC = $\angle$ABC = 180${}^{\circ }$

⇒ (2x + 15${}^{\circ }$) + (2x - 15${}^{\circ }$) = 180${}^{\circ }$
⇒ 4x${}^{\circ }$ = 180${}^{\circ }$
⇒ x = 45${}^{\circ }$

Therefore,

$\angle$ABD = 2x + 15${}^{\circ }$
= (2 × 45${}^{\circ }$) + 15${}^{\circ }$
= 90${}^{\circ }$ + 15${}^{\circ }$
= 105${}^{\circ }$

$\angle$DBC = 2x - 15${}^{\circ }$
= (2 × 45${}^{\circ }$) - 15${}^{\circ }$
= 75${}^{\circ }$

$\therefore$ $\angle$ABD = 105${}^{\circ }$ and $\angle$DBC = 75${}^{\circ }$