Question

Macy is trying to construct an isosceles triangle. She assigns an angle measurement of 40° to the unique angle of the triangle. She wants the length of the opposite side (the base) to be 6 centimeters. How many isosceles triangles can Macy construct using this information?

Answer 1

Macy can construct only one isosceles triangle using this information.

Step-by-step explanation:

An isosceles triangle has two equal angles and two equal sides.

If the unique angle of the triangle is 40°, the other two angles must be equal to each other. Since the sum of angles in a triangle is always 180°, the sum of the two equal angles is 180° - 40° = 140°.

Since the two equal angles are congruent, their measure is each 140° ÷ 2 = 70°.

The base of the triangle is opposite the unique angle. Since the length of the base is 6 centimeters, the length of each congruent side is also 6 centimeters.

Therefore, Macy can construct only one isosceles triangle using this information.