SOLUTION: If the meaning of an angle and its supplement are in the ratio 13:23, then the measure of the larger angle, in degrees, is: A) 65 B) 108 C) 115 D) 130 E) 144

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Question 1123473: If the meaning of an angle and its supplement are in the ratio 13:23, then the measure of the larger angle, in degrees, is:
A) 65
B) 108
C) 115
D) 130
E) 144

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

If the meaning of an angle and its supplement are in the ratio 13:23, then the measure of the larger angle, in degrees, is:
let’s an angle be alpha and its supplement beta
we know their sum is:
alpha%2Bbeta=180....eq.1
if their ratio 13%3A23, we have
alpha%3Abeta=13%3A23....eq.2
solve the system:
start with
alpha%2Bbeta=180....eq.1 and solve for alpha
alpha=180-beta....eq.1a
substitute in eq.2
%28180-beta%29%3Abeta=13%3A23....eq.2...solve for beta
23%28180-beta%29=13beta
4140-23beta=13beta
4140=13beta%2B23beta
4140=36beta
4140%2F36=beta
beta=115°

find alpha

alpha=180-beta....eq.1a
alpha=180-115
alpha=65°
so, the measure of the larger angle is: C) 115°