what is the angles

Question

The measure of one of the small angles of a right triangle is 66 more than 2 times the measure of the other small angle. Find the measure of both angles

smallest angle:

other non right angle:

Answer 1

Let "x" represent the size of one of the small angles. Let the other small angle be "y". Since this is a right triangle, the third angle is 90°. So, since the sum of the angles in every triangle is 180°, then x + y + 90° = 180° or y = 180° - 90° - x or y = 90° - x.

So one small angle is "x" and the other small angle is "90 - x"

We are told that "one of the small angles is 66 more than 2 times the other small angle". We can let "y" be the "other small angle", which means 2 times the other small angle is 2y and 66 more than that is 2y + 66.

So x = 2y + 66

But, we already know that y = 90° - x so:

x = 2(90 - x) + 66

x = 180 - 2x + 66

3x = 246

x = 246/3 = 82

So the one small angle is 82

The other small angle is 90 - x so it must be 90 - 82 = 8

That makes the smallest angle 8° and the other non-right angle is 82°