Question

If $△ABC\sim △DEF$ such that $\angle A={45}^o$ and $\angle E={56}^o$, then find the value of $\angle C$.

Answer 1

Since, $\Delta ABC\sim \Delta DEF$, then,

$\angle A=\angle D,\angle B=\angle E,\angle C=\angle F$

It is given that $\angle A={45}^{\circ }$ and $\angle E={56}^{\circ }$. As, $\angle E={56}^{\circ }$, then, $\angle B={56}^{\circ }$.

It is known that the sum of the angles of a triangle is ${180}^{\circ }$, therefore,

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

$\angle C={180}^{\circ }-\left(\angle A+\angle B\right)$

$={180}^{\circ }-\left({45}^{\circ }+{56}^{\circ }\right)$

$={79}^{\circ }$