Question

$\Delta ABC$ and $\Delta DEF$ are two similar triangles such that $\angle A={45}^{\circ },\angle E={56}^{\circ }$, then $\angle C$ =___.

• A. ${56}^{\circ }$
  
• B. ${45}^{\circ }$
  
• C. ${101}^{\circ }$
• D. ${79}^{\circ }$

Answer 1

Answer: (D)

${79}^{\circ }$

$\Delta ABC\sim \Delta DEF$ ...Given

$\Rightarrow \angle A=\angle D$ ...C.A.S.T.

$\Rightarrow \angle B=\angle E$ ...C.A.S.T.

$\Rightarrow \angle C=\angle F$ ...C.A.S.T.

$\therefore \angle B=\angle E={56}^o$

In $\Delta ABC$,

$\angle A+\angle B+\angle C={180}^o$ ....Angle sum property of triangles

$\Rightarrow {45}^o+{56}^o+\angle C={180}^o$

$\Rightarrow \angle C={79}^o$