The sum of all angles in a triangle is equal to 180. In the triangle given you have a right angle and the measure of a right angle is 90°. Based on that we can assume that 90°+ m∠2 + m∠3 = 180°. We can then derive a formula based on the given:
m∠2 = 3x
m∠3 = 2x
90°+ m∠2 + m∠3 = 180°
90°+ 3x + 2x = 180°
90° + 5x = 180°
Transpose the 90 to the other side of the equation:
5x = 180 - 90
5x = 90
Divide both sides of the equation by 5 to get x.
5x/5 = 90°/5
x = 18
Before we solve for the angles, you need to remember that angle 1 and angle 2 are supplementary. They make a straight line when combined and supplementary angles sum up to 180 as well.
Now let's solve for m∠2 since we know that x is equal to 18.
m∠2 = 3x
m∠2 = 3(18)
m∠2 = 54°
To get the m∠1, remember again that m∠1 + m∠2 = 180 because they are supplementary. With that equation you can now derive m∠1.
m∠1 + m∠2 = 180
m∠1 + 54 = 180
Transpose 54 to the other side of the equation. Don't forget to use the opposite operation.
m∠1 = 180-54
m∠1 = 126°
The answer is then A.
