Question

If in $△$s $ABC$ and $DEF,$ $\angle A=\angle E={37}^{\circ },AB:ED=AC:EF$ and $\angle F={69}^{\circ },$ then what is the value of $\angle B?$

• A. ${69}^{\circ }$
• B. ${74}^{\circ }$
• C. ${84}^{\circ }$
• D. ${94}^{\circ }$

Answer 1

Answer: (B)

${74}^{\circ }$

In $△ABC$ and $△DEF$
$\angle A=\angle E={37}^o$
$\frac{AB}{ED}=\frac{AC}{EF}$
Thus, $△ABC\sim △EDF$ ....... (By SAS rule)
Thus, $\angle B=\angle D$
Now, $△DEF$
$\angle D+\angle E+\angle F=180$
$\angle D+37+69=180$
$\angle D={74}^{\circ }$
Hence, $\angle B=\angle D={74}^{\circ }$