Answer:
I hope this helps.
Explanation:
In an isosceles trapezoid, the two non-parallel sides (legs) are congruent, and the base angles opposite each other are also congruent. Let's denote the measures of the angles as follows:
Angle A: The top left angle.
Angle B: The top right angle.
Angle C: The bottom left angle.
Angle D: The bottom right angle.
In an isosceles trapezoid, angles A and B are congruent, and angles C and D are congruent. The sum of the interior angles of any quadrilateral is 360 degrees. Therefore, we can set up the following equation:
Angle A + Angle B + Angle C + Angle D = 360 degrees
Since angles A and B are congruent, and angles C and D are congruent, we can rewrite the equation as:
2(A) + 2(C) = 360 degrees
Simplifying further:
2A + 2C = 360 degrees
Dividing both sides of the equation by 2:
A + C = 180 degrees
In an isosceles trapezoid, the base angles (C and D) are supplementary angles, meaning they add up to 180 degrees. Therefore, the measure of each base angle (C and D) is 180 degrees divided by 2:
Each base angle (C and D) = 90 degrees.
Since the sum of the interior angles in a quadrilateral is 360 degrees, and angles C and D (the base angles) each have a measure of 90 degrees, the sum of angles A and B (the top angles) must be:
Angle A + Angle B = 360 degrees - (Angle C + Angle D)
Angle A + Angle B = 360 degrees - (90 degrees + 90 degrees)
Angle A + Angle B = 360 degrees - 180 degrees
Angle A + Angle B = 180 degrees
Therefore, in an isosceles trapezoid, each top angle (A and B) has a measure of 180 degrees divided by 2:
Each top angle (A and B) = 90 degrees.
To summarize:
Each top angle (Angle A and Angle B) measures 90 degrees.
Each base angle (Angle C and Angle D) measures 90 degrees.