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: