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# Geometry

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Triangle ABC is isosceles with angle B congruent to angle C. The measure of angle C is five times the measure of angle A. What is the number of degrees in the measure of angle B?

Dec 19, 2021

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Triangle ABC is isosceles with angle B congruent to angle C. The measure of angle C is five times the measure of angle A. What is the number of degrees in the measure of angle B?

The sum of the three interior angles of any triangle is 180o

So A + B + C  =  180o

and B = C

and C = 5A

Since B = C and C = 5A, then B = 5A

Use substitution to get A + B + C all in terms of A

A + 5A + 5A  =  180o

[At this point I realized where it was going, and started having misgivings about my solution.  Usually, problems this easy are constructed to that the answer comes out even.  I've checked and double checked and doubled that again, and I can't see that I'm doing anything wrong.  So, I'm going to continue to the end.  But I'd feel a whole lot better if the problem had said that C is four times A.]

So 11A = 180o  which means that A = 180/11 degrees

Since B = 5A, then B = 900/11 degrees  or in decimal form, approximately 81.82 degrees

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Dec 19, 2021