Triangle XYZ is an isosceles triangle with sides XY = XZ. If the measure of angle Y is 80°, what is the measure of angle X?

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Accepted Answer

Given triangle XYZ is isosceles with XY = XZ, so angles opposite these sides are equal. Therefore, angle Y = angle Z.

Given angle Y = 80°, so angle Z = 80°.

Sum of angles in a triangle = 180°.

So, angle X + angle Y + angle Z = 180°
=> angle X + 80° + 80° = 180°
=> angle X + 160° = 180°
=> angle X = 180° - 160° = 20°.

However, this contradicts the options given. Let's re-check the logic:

Since XY = XZ, angles opposite these sides are equal, so angle Y = angle Z.

Given angle Y = 80°, so angle Z = 80°.

Sum of angles = 180°

angle X + 80° + 80° = 180°

angle X = 180° - 160° = 20°.

The correct measure of angle X is 20°, which corresponds to option 3.

Therefore, the correct answer is 20°.

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