Question

In figure lines $l_1$ and $l_2$ intersect at O, forming angles as shown in the figure.If $a={35}^{\circ }$, find the values of b, c and d. [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 0.5 Mark
Answer: 0.5 Mark each

Since lines $l_1$ and $l_2$ intersect at O.

$\angle a=\angle c$ [Vertically opposite angles]

$\Rightarrow \angle c={35}^{\circ }$ $[\angle a={35}^{\circ }]$

$\angle a+\angle b={180}^{\circ }$ [Linear pair of angles]

$\Rightarrow {35}^{\circ }+\angle b={180}^{\circ }$

$\Rightarrow \angle b={145}^{\circ }$

Since $\angle b$ and $\angle d$ are vertically opposite angles.

$\Rightarrow \angle d=\angle b$

$\Rightarrow \angle d={145}^{\circ }$ $[\angle b={145}^{\circ }]$

Hence, $\angle b={145}^{\circ },\angle c={35}^{\circ },\angle d={145}^{\circ }$