A right triangle has acute angles measuring 2x+6 degrees and 3x−26 degrees. Use the Triangle Angle Sum Theorem to find the measures of the missing angles of the triangle.

Answer 1

First, we know that the sum of the angles in any triangle is always 180 degrees. So, we can set up an equation using the given angle measures:

(2x+6) + (3x-26) + A = 180

Combining like terms:

5x - 20 + A = 180

Now, solve for A:

A = 180 - 5x + 20
A = 200 - 5x

Now, we can find the missing angles in the triangle by plugging in this expression for A:

1. Angle A = 200 - 5x
2. Angle B = 2x + 6
3. Angle C = 3x - 26

Now, we know that angle A is one of the acute angles, so we must choose the smallest angle for A. The remaining angles will be B and C.

So, we need to find the value of x that makes angle A the smallest of the three angles.

Setting up an inequality:

200 - 5x < 2x + 6
194 < 7x
x > 194/7

Now, we can substitute this value of x back into the expressions for angles B and C to find their measures.