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Question 1-5 An Isosceles Trapezoid ABCD Has Two Parallel Sides Overline (AB) and Overline (CD) Enter a Number in Each Box to Complete

Question

Question 1-5 An isosceles trapezoid ABCD has two parallel sides overline (AB) and overline (CD) Enter a number in each box to complete the sentences. If the measure of angle A is equal to 65 degrees, the measure of angle D is square degrees. The sum of measures of angles B and C is square degrees. The sum of measures of angles A and C is square degrees If the measure of angle A is equal to 45 degrees, the measure of angle B is square degrees

Answer

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Luan Elite · Tutor for 8 years

Answer

### If the measure of angle is equal to 65 degrees, the measure of angle is 65 degrees.### The sum of measures of angles and is 230 degrees.### The sum of measures of angles and is 180 degrees.### If the measure of angle is equal to 45 degrees, the measure of angle is 135 degrees.

Explanation

## Step 1: Understanding the properties of an isosceles trapezoid### In an isosceles trapezoid, the two non-parallel sides (legs) are of equal length, and the base angles (angles adjacent to each base) are equal.## Step 2: Calculating the measure of angle given angle ### Since angles and are on the same side and the trapezoid is isosceles, angle equals angle , therefore degrees.## Step 3: Calculating the sum measures of angles and ### The sum of the interior angles of any quadrilateral is 360 degrees. Given angles and are each 65 degrees, we calculate the sum of and as follows: ## Step 4: Calculating the sum measures of angles and ### If angle : ## Step 5: Calculating the measure of angle given angle degrees### Since angle and angle are equal: