Bunuel wrote:

In isosceles triangle XYZ above, angle XYZ measures 100 degrees. What is the measure of angle XZY?

A. 40

B. 45

C. 60

D. 100

E. Cannot be determined

Attachment:

Triangle_X_Y_Z.png

We'll show two solutions:

The first is a Logical approach, based on the general properties of triangles.

An isosceles triangle has two equal angles. Since our triangle cannot have two angles equal to 100 (as then the sum of its angles would be more than 180) then 100 must be the angle of the head of the triangle and the two base angles are (180 - 100)/2 = 40.

(A) is our answer.

Another approach is Alternative: since the possible options are right in front of us, why not use them?

If A. were true then one angle would be 100, the other 40 so the last is 180 - 40 -100 = 40 and the triangle is isosceles.

Could work, let's check the others.

If B. were true then the third angle is 180 - 45 - 100 = 35 and the triangle is not isosceles. No.

If C were true then the third angle is 180 - 60 - 100 = 20 and the triangle is not isosceles. No.

If D. were true then the third angle is 180 - 100 - 100 <0 which is impossible. No.

We've tried all the given options and should feel comfortable selecting (A).

_________________

David

Senior tutor at examPAL

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