Question

If in the $△$'s ABC and DEF, $\angle$A is equal to $\angle$E, both are equal to ${40}^{\circ }$. AB : ED = AC : EF and angle F is ${65}^{\circ }$, then angle B is:

• A. 35º
• B. 65º
• C. 75º
• D. 85º

Answer 1

The correct option is C

75º

AB : ED = AC : EF $\Rightarrow$ $△$ABC is similar to $△$EDF.

Now, $\angle$A = $\angle$E = ${40}^{\circ }$, $\angle$C = $\angle$F = ${65}^{\circ }$

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