In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what type of

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Question: In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what type of triangle is it?

Options:

Correct Answer: Isosceles

Solution:

Since two angles are equal, triangle XYZ is an isosceles triangle.

In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what type of triangle is it?

In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what type of triangle is it?

Step 1: Identify the angles given in triangle XYZ. We have angle X = 45 degrees and angle Y = 45 degrees.
Step 2: Recall that a triangle has three angles that add up to 180 degrees.
Step 3: Calculate the third angle (angle Z) using the formula: angle Z = 180 - (angle X + angle Y).
Step 4: Substitute the values: angle Z = 180 - (45 + 45) = 180 - 90 = 90 degrees.
Step 5: Now we have angle X = 45 degrees, angle Y = 45 degrees, and angle Z = 90 degrees.
Step 6: Since two angles (X and Y) are equal, triangle XYZ is classified as an isosceles triangle.

Triangle Properties – Understanding the properties of triangles, specifically that a triangle with two equal angles is isosceles.
Angle Sum Property – Recognizing that the sum of angles in a triangle is always 180 degrees.