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

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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 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 1

### If the measure of angle \( A \) is equal to 65 degrees, the measure of angle \( D \) is 65 degrees. ### The sum of measures of angles \( B \) and \( C \) is 230 degrees. ### The sum of measures of angles \( A \) and \( C \) is 180 degrees. ### If the measure of angle \( A \) is equal to 45 degrees, the measure of angle \( B \) is 135 degrees.

Answer 2

## 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 \( D \) given angle \( A \) ### Since angles \( A \) and \( D \) are on the same side and the trapezoid is isosceles, angle \( D \) equals angle \( A \), therefore \( D = 65 \) degrees. ## Step 3: Calculating the sum measures of angles \( B \) and \( C \) ### The sum of the interior angles of any quadrilateral is 360 degrees. Given angles \( A \) and \( D \) are each 65 degrees, we calculate the sum of \( B \) and \( C \) as follows: \[ \text{Sum of angles } A \text{ and } D = 65^\circ + 65^\circ = 130^\circ \] \[ 360^\circ - 130^\circ = 230^\circ \] ## Step 4: Calculating the sum measures of angles \( A \) and \( C \) ### If angle \( A = 65^\circ \): \[ \text{Sum of angles } A \text{ and } C = 65^\circ + 115^\circ = 180^\circ \] ## Step 5: Calculating the measure of angle \( B \) given angle \( A = 45 \) degrees ### Since angle \( A \) and angle \( D \) are equal: \[ D = 45^\circ \] \[ \text{Sum of } \, A \text{ and } D = 45^\circ + 45^\circ = 90^\circ \] \[ 360^\circ - 90^\circ = 270^\circ \] \[ \text{Since A and B are on the same side of the base and the trapezoid sides } \overline{AB} \text{ and } \overline{CD} \text{ are parallel:} \] \[ \, B = 180^\circ - A = 180^\circ - 45^\circ = 135^\circ \]

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