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HiSET: Math : Solve problems

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Example Question #1 : Measurement And Geometry

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?

Possible Answers:

$66 \frac{2}{3} ^{\circ }$ $\displaystyle 66 \frac{2}{3} ^{\circ }$

$56 \frac{2}{3} ^{\circ }$ $\displaystyle 56 \frac{2}{3} ^{\circ }$

$73\frac{1}{3}^{\circ }$ $\displaystyle 73\frac{1}{3}^{\circ }$

$63 \frac{1}{3} ^{\circ }$ $\displaystyle 63 \frac{1}{3} ^{\circ }$

$53 \frac{1}{3} ^{\circ }$ $\displaystyle 53 \frac{1}{3} ^{\circ }$

Correct answer:

$66 \frac{2}{3} ^{\circ }$ $\displaystyle 66 \frac{2}{3} ^{\circ }$

Explanation:

Let $\displaystyle x$ 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 x- 10 $\displaystyle x- 10$. The sum of the measures of the angles of a triangle is 180 degrees, so

$\displaystyle x+ (x-10) + (x-10) = 180$

To solve for $\displaystyle x$, first ungroup and collect like terms:

$\displaystyle x+ x - 10 + x - 10 = 180$

$\displaystyle x+ x + x - 10 - 10 = 180$

$\displaystyle 3x - 20 = 180$

Isolate $\displaystyle x$; first add 20:

$\displaystyle 3x-20+20 = 180 + 20$

3x= 200 $\displaystyle 3x= 200$

Divide by 3:

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

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

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

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

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HiSET: Math : Solve problems

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Example Question #1 : Measurement And Geometry

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