SOLUTION: The sum of two angles is 92∘. Angle 2 is 123∘ smaller than 4 times angle 1. What are the measures of the two angles in degrees?

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Question 867200: The sum of two angles is 92∘. Angle 2 is 123∘ smaller than 4 times angle 1.
What are the measures of the two angles in degrees?
Answer by MathLover1(20850) About Me  (Show Source):
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The sum of two angles is 92∘. Angle 2 is 123∘ smaller than 4 times angle 1.
What are the measures of the two angles in degrees?

let angle 1 be alpha and angle 2 beta
given:
alpha%2Bbeta=92....eq.1
beta%2B123=4alpha =>
beta=4alpha-123...eq.2...plug in eq.1

alpha%2B4alpha-123=92...solve for alpha
5alpha=92%2B123
5alpha=+215
alpha=+215%2F5
highlight%28alpha=+43%29°
now, back to eq.2 and find beta
beta=4alpha-123
beta=4%2A43-123
beta=172-123
highlight%28beta=49%29°