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The triangle is obtuse and the two sides of the triangle are congruent. The measure of one of the base angles is 1/6 times the difference of the vertex angle and one of its base angles. Find the measure of all three angles.

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Answer:

base angles = 20° each;

vertex angle = 140°

Step-by-step explanation:

let: x be the vertex angle

y be the base angles

sum of angles of a triangle in 180°

x+y+y=180

x+2y=180, this is your eq. 1

The measure of one of the base angles is 1/6 times the difference of the vertex angle and one of its base angles, so

y=(x-y)/6

[y=(x-y)/6]*6

6y=x-y

x-y-6y=0

x-7y=0

x=7y, substitute this to eq. 1

x+2y=180

7y+2y=180

9y=180

y=20

x+2y=180

x+2(20)=180

x-40=180

x=140

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