Question

Two rays are drawn from a point 'P' on a line as shown. If angle 'a' and 'c' are equal and twice that of angle 'b'. Then find angle 'b'.

• A. ${36}^{\circ }$
• B. ${12}^{\circ }$
• C. ${72}^{\circ }$
• D. ${18}^{\circ }$

Answer 1

The correct option is A

${36}^{\circ }$

Let the value of angle 'b' be 'x'

Then angle 'a' = angle 'c' = 2x

Sum of all angles at a point on the same side of a line is ${180}^{\circ }$

So, $\angle$a + $\angle$b +$\angle$c = ${180}^{\circ }$

$\Rightarrow$ 2x + 2x +x = ${180}^{\circ }$

$\Rightarrow$ 5x = ${180}^{\circ }$

$\Rightarrow$ x = ${36}^{\circ }$.