Mr.soto drew a design for a quilting pattern. The design is made up of 5 congruent isosceles trapezoids as shown below. What is the measure, in degrees, of angle y?
Do you really think we can see this (with our crystal ball)?
•find the measure of one of the interior angles
180(3)/5 =108
•y is NOT the exterior angle
•use the formula:
360-a=2y
*where a= the measurement of 1 of the interior angles which is 108 in this case.
•so it would be:
360-108=2y
252=2y
252/2=y
126=y
•so y=126
To find the measure of angle y, we first need to determine the measure of the base angles of the isosceles trapezoid.
An isosceles trapezoid has two congruent base angles (let's call them A and B) and two congruent non-base angles (let's call them X and Y). In the given design, the isosceles trapezoid has an angle labeled X and an angle labeled Y.
Since all the trapezoids in the design are congruent, the measures of the base angles A and B are the same for all trapezoids. Therefore, let's assume angle A is the measure of the base angles for one trapezoid.
Since the sum of the angles in a trapezoid is 360 degrees, we can write the equation: A + A + Y + X + Y = 360 degrees.
Since A is a measure of the base angles, it is equal to 180 - Y degrees (the supplementary angle to angle Y).
Substituting these values into the equation, we get: (180 - Y) + (180 - Y) + Y + X + Y = 360 degrees.
Simplifying the equation, we get: 2(180 - Y) + 2Y + X = 360 degrees.
Expanding the equation, we get: 360 - 2Y + 2Y + X = 360 degrees.
Combining like terms, we get: X = 0 degrees.
Therefore, the measure of angle y (Y) is 0 degrees.