Question

In the figure, ray AD stands on the line CB, $\angle BAD=(2x+10{)}^{\circ }$ and $\angle CAD=(5x+30{)}^{\circ }$, find the valve of x and also write $\angle BAD$ and $\angle CAD$. [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

$\angle BAD+\angle CAD={180}^{\circ }$ (linear pair of angles)

$⟹$ $(2x+{10}^{\circ })+(5x+30{)}^{\circ }={180}^{\circ }$

$⟹$ $(7x+40{)}^{\circ }={180}^{\circ }$

$⟹$ $7x={180}^{\circ }-{40}^{\circ }$

$⟹7x={140}^{\circ }$

$⟹$ $x=\frac{140}{7}$

$⟹$ $x=20$

$\angle BAD=(2\times {20}^{\circ })+{10}^{\circ }={50}^{\circ }$

$\angle CAD=(5\times {20}^{\circ })+{30}^{\circ }={130}^{\circ }$