The measures of the three angles of a triangle are in the... | SAT Lines, angles, and triangles Question, Answer Explained

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Math · Geometry and TrigonometryEasy

The measures of the three angles of a triangle are in the ratio $2:3:7$ . What is the measure of the largest angle?

$15^\circ$

$45^\circ$

$105^\circ$

$210^\circ$

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Answer: C

Write the angle measures as $2k$ , $3k$ , and $7k$ degrees. They sum to $180^\circ$ , so $12k = 180$ and $k = 15$ . The largest angle measures $7k = 7(15) = 105^\circ$ .

Choice A is the value of one part of the ratio, $k$ , not the measure of the largest angle.

Why the other choices are wrong

A. 15 degrees is one part of the ratio, not the largest angle.
B. 45 degrees is the middle angle, 3 parts.
D. This uses 360 degrees, but a triangle's angles sum to 180 degrees.

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