Question

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.(4 points) describe in the wording of 7th grader make sure its only text too

Answer 1

Sure! In a right triangle, one angle is always 90 degrees, and the sum of all angles in a triangle is always 180 degrees!

In this triangle, we have two other angles that are measured as 2x + 6 degrees and 3x - 26 degrees. Since the triangle has a right angle (90 degrees), we can use the Triangle Angle Sum Theorem to help us find the values of x and ultimately the measures of the other angles.

First, we know that the total of the angles should equal 180 degrees. So, we can write this equation:

(2x + 6) + (3x - 26) + 90 = 180.

Now, let’s combine the like terms:

2x + 3x + 6 - 26 + 90 = 180.

This simplifies to:

5x + 70 = 180.

Next, we’ll subtract 70 from both sides to isolate the term with x:

5x = 180 - 70,

which simplifies to:

5x = 110.

Now, we divide both sides by 5 to find x:

x = 110 / 5,

which means

x = 22.

Now that we have x, we can plug it back into the expressions for the two angles:

For the first angle, 2x + 6:
2(22) + 6 = 44 + 6 = 50 degrees.

For the second angle, 3x - 26:
3(22) - 26 = 66 - 26 = 40 degrees.

So, the three angles in the triangle are:

1. 90 degrees (the right angle),
2. 50 degrees,
3. 40 degrees.

Now we have found all the angles in the right triangle! The measures of the angles are 90 degrees, 50 degrees, and 40 degrees.