To find the measure of the larger of the two angles when one angle is 40° greater than 3 times its supplement, we need to set up and solve the equation based on the relationship between the angles.
Step-by-step solution:
1. Let one angle be denoted as [tex]\( x \)[/tex]. Its supplement is then [tex]\( 180° - x \)[/tex].
2. According to the problem, the angle [tex]\( x \)[/tex] is 40° greater than 3 times its supplement. This relationship can be expressed mathematically as:
[tex]\[
x = 3(180° - x) + 40°
\][/tex]
3. Distribute the 3 on the right-hand side of the equation:
[tex]\[
x = 540° - 3x + 40°
\][/tex]
4. Combine like terms on the right-hand side to get:
[tex]\[
x = 580° - 3x
\][/tex]
5. To solve for [tex]\( x \)[/tex], first add [tex]\( 3x \)[/tex] to both sides of the equation to get all [tex]\( x \)[/tex] terms on one side:
[tex]\[
x + 3x = 580°
\][/tex]
6. Combine like terms on the left-hand side:
[tex]\[
4x = 580°
\][/tex]
7. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 4:
[tex]\[
x = \frac{580°}{4}
\][/tex]
8. Simplify the division:
[tex]\[
x = 145°
\][/tex]
So, the measure of one angle ([tex]\( x \)[/tex]) is 145°.
9. The supplement of the angle is:
[tex]\[
180° - x = 180° - 145° = 35°
\][/tex]
10. Now, to determine the larger of the two angles, compare the two values:
- [tex]\( x = 145° \)[/tex]
- [tex]\( 180° - x = 35° \)[/tex]
11. Clearly, the larger angle is [tex]\( 145° \)[/tex].
Therefore, the measure of the larger of the two angles is [tex]\( 145° \)[/tex].
