Question

If ABC and DEF are similar triangles such that $\angle A={47}^{\circ }$ and $\angle B={83}^{\circ }$ then $\angle F$ is

• A. ${60}^{\circ }$
• B. ${70}^{\circ }$
• C. ${50}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

Answer: (C)

${50}^{\circ }$

Since triangle ABC and DEF are similar

$\therefore \angle A=\angle D,\angle B=\angle Eand\angle C=\angle F$

In $△ABC$

$\angle A+\angle B+\angle C={180}^{\circ }$

${47}^{\circ }+{83}^{\circ }+\angle C={180}^{\circ }$

$\angle C={180}^{\circ }-{130}^{\circ }$

$\angle C={50}^{\circ }$

$\therefore \angle F={50}^{\circ }$