SOLUTION: In a certain triangle the measure of one angle is double the measure of a second angle but is 5 degrees less than the measure of the third angle. If the sum of the measures of the

Question 160705This question is from textbook
: In a certain triangle the measure of one angle is double the measure of a second angle but is 5 degrees less than the measure of the third angle. If the sum of the measures of the three interior angles of a triangle is always 180 degrees, form an algebraic equation to express the problem, and identify the variables, coefficients, and constants of the alegbraic expression. This question is from textbook

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In a certain triangle the measure of one angle is double the measure of a second angle but is 5 degrees less than the measure of the third angle. If the sum of the measures of the three interior angles of a triangle is always 180 degrees, form an algebraic equation to express the problem, and identify the variables, coefficients, and constants of the algebraic expression.
:
Let the angles be A, B, C
:
Write an equation for each statement:
:
"the measure of one angle is double the measure of a second angle"
A = 2B
or
B = .5A
:
" but is 5 degrees less than the measure of the third angle."
A = C-5
or
C = (A+5)
:
"If the sum of the measures of the three interior angles of a triangle is always 180 degrees,":
A + B + C = 180
:
form an algebraic equation to express the problem, and identify the variables, coefficients, and constants of the algebraic expression.
:
Substitute for B and C
A + .5A + (A+5) = 180
2.5A = 180 - 5
2.5A = 175
solve
A =
A = 70 degrees, B = 35, C = 75
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