Question

In $△$ ABC and $△$ DEF, $\angle$A = $\angle$E = ${40}^{\circ }$ and $\frac{AB}{ED}$ = $\frac{AC}{EF}$. Find $\angle$B if $\angle$F is ${65}^{\circ }$.

• A. ${35}^{\circ }$
• B. ${65}^{\circ }$
• C. ${75}^{\circ }$
• D. ${85}^{\circ }$

Answer 1

The correct option is C

${75}^{\circ }$

$\frac{AB}{ED}$ = $\frac{AC}{EF}$ (Given)
$\angle$A = $\angle$E = ${40}^{\circ }$

Since, the ratio of adjacent sides and the included angles are equal.
$\therefore △$ABC is similar to $△$EDF by SAS similarity criterion.

Now, $\angle$C = $\angle$F = ${65}^{\circ }$ [Corresponding angles of a similar triangles are equal]

$\therefore$ $\angle$B = ${180}^{\circ }-(\angle A+\angle C$)
$={180}^{\circ }$ - (${40}^{\circ }$ + ${65}^{\circ }$ )= ${75}^{\circ }$