Question

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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

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The measure of the missing angle of the triangle is 22 degrees.

Explanation:

a = 2x+6 degrees b = 3x−26 degrees

a° + b° + 90° = 180° (right angle triangle)

(2x+6)° + (3x−26)° + 90° = 180°

(2x + 3x)° - 26° + 6° + 90 = 180°

5x° - 20° + 90 = 180°

5x° + 70° = 180°

5x° + 70° - 70 = 180° -70

5x° = 110°

5x° ÷ 5 = 110° ÷ 5

x = 22 degrees

Answer 2

The Triangle Angle Sum Theorem states that the sum of the angles in any triangle is always 180 degrees. Therefore, we can use this theorem to find the measure of the missing angle in the right triangle.

Since we know that one of the angles in the right triangle is a right angle and measures 90 degrees, we can set up an equation to solve for the other two angles:

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

Simplifying the equation, we get:

5x - 20 = 90

Adding 20 to both sides, we get:

5x = 110

Dividing by 5, we get:

x = 22

Now that we know the value of x, we can substitute it back into the expressions for the two angles to find their measures:

2x+6 = 50 degrees

3x-26 = 40 degrees

Therefore, the measures of the missing angles in the right triangle are 40 degrees and 50 degrees.