Question

In the figure above, three lines intersect at a point.
If $f={85}^o$ and $c={25}^o$, what is the value of $a$?

• A. ${60}^o$
• B. ${65}^o$
• C. ${70}^o$
• D. ${75}^o$

Answer 1

Answer: (C)

${70}^o$

In the given diagram, $\angle c={25}^0$ and $\angle f={85}^0$

$\Rightarrow \angle c=\angle g$ .....( vertical opposite angle)

similarly $\angle a=\angle e$ .....( vertical opposite angles)

The sum of the angles in straight lines $={180}^0$

$\angle g+\angle f+\angle e={180}^0$

$\Rightarrow 25+85+\angle e=180$

$\Rightarrow 110+\angle e=180$

$\Rightarrow \angle e=180-110$

$\Rightarrow \angle e=70$

$\Rightarrow \angle e=\angle a$

$\Rightarrow \angle a={70}^0$