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If the degree measures of two angles of an...

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by swerve » Mon Oct 30, 2017 9:08 am
If the degree measures of two angles of an isosceles triangle are in the ratio 1:3, what is the degree measure of the largest angle if it is not a base angle?

(A) 26°
(B) 36°
(C) 51°
(D) 92°
(E) 108°

The OA is E.

Can any expert help me with this PS question please? I don't have it clear. Thanks.
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by [email protected] » Mon Oct 30, 2017 2:25 pm
Hi swerve,

We're told that two angles of an ISOSCELES triangle are in the ratio 1:3. We're asked for the degree measure of the LARGEST angle if it is not a base angle.

Since we're dealing with an ISOSCELES triangle, we know that two of the angles are the SAME. Thus, the ratio of the angles is either 1:1:3 or 1:3:3. We're told that the largest angle is NOT one of the two base angles, so we're dealing with the first possibility (in which the angles can be referred to as X, X and 3X). In that triangle we have....

5X = 180 degrees
X = 36 degrees
The three angles are 36, 36 and 108

Final Answer: E

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