Question

5] if triangle ABC ~ triangleDEF and angle A= 45°angle E =85° then find angle C and angle F​

Answer 1

The value of \angle∠ C = 50°.

Step-by-step explanation:

We are given that triangle ABC is similar to triangle DEF such that angle A = 45 degrees and Angle B = 85 degrees.

And we have to find the value of angle C.

Since \triangle△ ABC ~ \triangle△ DEF, this means that;

\angle∠ A = \angle∠ D, \angle∠ B = \angle∠ E and \angle∠ C = \angle∠ F

As we know that the angle sum property of the triangle says: The sum of all angles of the triangle is equal to 180°.

So, In \triangle△ ABC,

\angle∠ A + \angle∠ B + \angle∠ C = 180°

Here we are given \angle∠ A = 45° and \angle∠ B = 56°, that means;

45° + 85 + \angle∠ C = 180°

130° + \angle∠ C = 180°

\angle∠ C = 180° - 130° = 50