Question

If ∆ABC ~ ∆DEF and ∠A = 43°,∠B =54° then ∠F =​

Answer 1

Answer:

87°

Step-by-step explanation:

Given:

$\triangle ABC \sim \triangle DE F$

So,

$\angle A = \angle D = 43^{\circ} \\\angle B = \angle E = 54^{\circ}\\\angle C = \angle F =\:\:\: ?$

To Find:

$\angle C = \angle D =\:\: ?$

In ΔABC,

We know that,

Sum of all angles of a triangle = 180°

$\implies\angle A\:+\:\angle B\:+\:\angle C = 180^{\circ}\\\implies\:43^{\circ}\:+\: 54^{\circ}\:+\:\angle C = 180^{\circ}\\\implies\:\:\:\:\:\:\:\:\:\:\:\:\:\:97^{\circ}\:+\:\angle C = 180^{\circ}\\\implies\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\ \angle C = 180^{\circ}-97^{\circ}\\ \therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\ \ C = 87^{\circ}$

Now,

∠C = ∠F = 87°