Solve problems - HiSet: High School Equivalency Test: Math

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Question

Two of the angles of a triangle are congruent; the third has measure ten degrees greater than either one of the first two. What is the measure of the third angle?

Answer

Let be the measure of the third angle. Since its measure is ten degrees greater than either of the others, then the common measure of the other two is . The sum of the measures of the angles of a triangle is 180 degrees, so

To solve for , first ungroup and collect like terms:

Isolate ; first add 20:

Divide by 3:

$3x \div 3 = 200 \div 3$

Since $200 \div 3 = 66 \textup{ R }2$ ,

$x = 66 \frac{2}{3}$ .

The third angle measures $66 \frac{2}{3} ^{\circ }$ .

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