Two supplementary angles have measurements of (3x)° and (10x – 15)°. What are the measures of the two angles?
Mathematics · High School · Thu Feb 04 2021
Answered on
Given:
Angle 1 = 3x
Angle 2 = 10x - 15
Find the measurement of the two angles, if the two angles are supplementary.
Solution:
Supplementary angles, are angles that add up to 180 degrees, hence we can equate the two equations into one single solution separated by a plus sign and having a sum of 180.
(3x) + (10x - 15) = 180
Now in order to find the angles we simply need to solve for x.
3x + 10x - 15 = 180
13x - 15 = 180
Transpose -15 to the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.
13x = 180 + 15
13x = 195
Divide both sides by 13 in order to cancel out 13x, leaving behind x.
13x/13 = 195/13
x = 15
Angle 1 = (3)(15)
Angle 1 = 45°
Angle 2 = 10 (15) - 15
Angle 2 = 135°
Final answer:
Angle 1 = 45°
Angle 2 = 135°