Question

From the figure, find values of $x$ and $y$.

• A. ${25}^o,{30}^o$
• B. ${35}^o,{31}^o$
• C. ${50}^o,{28}^o$
• D. ${45}^o,{33}^o$

Answer 1

Answer: (D)

${45}^o,{33}^o$

In the given triangle,

by angle sum property,

${40}^o+{95}^o+x^o={180}^o.......\left(i\right)$

and $x^o+y^o+{102}^o={180}^o.......\left(ii\right)$.

From $\left(i\right)$,

${40}^o+{95}^o+x^o={180}^o$

$⟹$ ${135}^o+x^o={180}^o$

$⟹$ $x^o={180}^o-{135}^o$

$⟹$ $x^o={45}^o.......\left(iii\right)$.

Substitute $\left(iii\right)$ in $\left(ii\right)$,

${45}^o+y^o+{102}^o={180}^o$

$⟹$ $y^o+{147}^o={180}^o$

$⟹$ $y^o={180}^o-{147}^o$

$⟹$ $y^o={33}^o$.

Therefore, $x^o={45}^o$ and $y^o={33}^o$.

Hence, option $D$ is correct.