Question

In $\Delta ABC$ and $\Delta DEF$, $\angle A=\angle E={40}^{\circ }$, AB : ED = AC : EF and $\angle F={65}^{\circ }$, then the value of $\angle B$ is

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

Answer 1

The correct option is C

${75}^{\circ }$

In $\Delta ABC$ and $\Delta DEF$,
$\angle A=\angle E$ (Given)
$\frac{AB}{ED}=\frac{AC}{EF}$ (Given)
By SAS Criteria,
$\Delta ABC\sim \Delta EDF\therefore \angle A=\angle E,\angle B=\angle D,\angle C=\angle F$
Now, In $\Delta ABC$,
$\angle A={40}^{\circ }$ [Given]
$\angle C={65}^{\circ }[\because \angle C=\angle F={65}^{\circ }]$
$\angle A+\angle B+\angle C={180}^{\circ }$ (Sum of the angles in a $\Delta$ is 180${}^{\circ }$)

On substituting the values we get:
${40}^{\circ }+\angle B+{65}^{\circ }={180}^{\circ }$
$\angle B={180}^{\circ }-{40}^{\circ }-{65}^{\circ }$
$\angle B={75}^{\circ }$