Respuesta :
Answer:
The measure of the larger is [tex]133^{\circ}[/tex].
Step-by-step explanation:
Given:
The measure of an angle is [tex]8[/tex] degrees less than three times the measure of another angle.
The two angles are supplementary.
To find: The measure of the larger angle.
Solution:
Let the measure of the smaller angle be [tex]x^{\circ}[/tex].
Then the measure of the larger angle be [tex]3x^{\circ}-8^{\circ}[/tex].
The two angles are supplementary, so their sum is [tex]180^{\circ}[/tex].
So, [tex]x^{\circ}+3x^{\circ}-8^{\circ}=180^{\circ}[/tex]
[tex]\Rightarrow 4x^{\circ}-8^{\circ}=180^{\circ}[/tex]
[tex]\Rightarrow 4x^{\circ}=180^{\circ}+8^{\circ}[/tex]
[tex]\Rightarrow 4x^{\circ}=188^{\circ}[/tex]
[tex]\Rightarrow x^{\circ}=\frac{188^{\circ}}{4}[/tex]
[tex]\Rightarrow x^{\circ}=47^{\circ}[/tex]
So, the measure of the smaller angle is [tex]47^{\circ}[/tex].
And, the measure of the larger angle is [tex]3\times47^{\circ}-8^{\circ}=133^{\circ}[/tex].
Hence, the measure of the larger is [tex]133^{\circ}[/tex].
