MATH SOLVE

10 months ago

Q:
# In a right triangle, he measure of one acute angle is 3 times the sum of the other acute angle and 8, Find the measure of angle 1 and 2

Accepted Solution

A:

Let the acute angles be x and y respectively. x= 3(y+8).

The sum of the interior angles of a triangle is always 180 degrees. Therefore, 90 + y + 3(y+8) = 180, and so y + 3y + 24 = 90 => 4y= 66, and y = 66/4 = 16.5 degrees.

Let's check: If we're right, then y + 3(y+8) = 90

16.5 + 3(16.5 + 8) = 90 ?

Yes. (check it yourself)

Thus, the 3 angles of this right triangle are 90, 16.5 and 73.5; they add up to 180 degrees.

The sum of the interior angles of a triangle is always 180 degrees. Therefore, 90 + y + 3(y+8) = 180, and so y + 3y + 24 = 90 => 4y= 66, and y = 66/4 = 16.5 degrees.

Let's check: If we're right, then y + 3(y+8) = 90

16.5 + 3(16.5 + 8) = 90 ?

Yes. (check it yourself)

Thus, the 3 angles of this right triangle are 90, 16.5 and 73.5; they add up to 180 degrees.