Question

In the given figure, find 𝑥. Further find ∠𝐵𝑂𝐶, ∠𝐶𝑂𝐷 and ∠𝐴𝑂𝐷.

Answer 1

Step 1:
“ If a ray stands on a line, the sum of two adjacent angles formed is always 180°”. This is known as the Linear pair axiom.


Step 2:
Simplify the Equation.
∠AOC + ∠COB = 180°
But, ∠COB = ∠COD + ∠DOB
= $x$ + $x$ + ${20}^o$
=$2x$ + ${20}^o$
∠AOC + ∠COB =${180}^o$
x+10°+ 2x+20°= ${180}^o$
$3x$ +${30}^o$=${180}^o$
$3x$ =${150}^o$
$x$ =$\frac{{150}^o}{3}$
$x$ =${50}^o$
Hence, $x$ =${50}^o$

Step 3:
substitute the value of
$x$ to find the measure of angles.

∠𝐵𝑂C = $(x+{20}^o)$
∠𝐵𝑂C = $({50}^o+{20}^o)$ = ${70}^o$
∠𝐶𝑂𝐷 = $x$ = ${50}^o$
∠𝐴𝑂𝐷 = $(x+{10}^o)$
∠𝐴𝑂𝐷 = $({50}^o+{10}^o)$ = ${60}^o$

Verification

${70}^o+{50}^o+{60}^o={180}^o$