SOLUTION: The measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles. Write and solve a system of equations to find the measu

Question 1035845: The measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles. Write and solve a system of equations to find the measures of all the angles.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
A trapezoid (in some languages) is a quadrilateral with two parallel sides.
In general, all four angles could have different measures,
but the angles attached to each non-parallel side are supplementary,
meaning that their measures add up to .

In this case, the acute angles have the same measure, ,
and so do the obtuse angles, because it is an isosceles trapezoid.

= four times the measures (in degrees) of the acute angles;
= five more than the measures (in degrees) of the acute angles,
and the problem says that
,
so all we have to do is solve that equation.

---> --->
So the acute angles measure ,
and the obtuse angles measure .
RELATED QUESTIONS
The measures of the angles in a triangle are x, 2x, and 3x. The triangle is acute... (answered by Edwin McCravy)

The measures of the angles in a triangle are x, 2x, and 3x. The triangle is acute,... (answered by josgarithmetic)

the sum of the measures of an obtuse angle and an acute angle is 160.the sum of the... (answered by stanbon)

The sum of the measures of two angles is 120 degrees .If the measure of one of the angles (answered by rapaljer)

The sum of the measures of an acute angle and an obtuse angle is 150 degrees. The sum of... (answered by ankor@dixie-net.com)

In a right triangle, one of the acute angles is fourteen times as large as the other... (answered by checkley77)

The measures of two angles in a trapezoid are in the ratio of 2:4. The measure of the... (answered by TimothyLamb)

The sum of the measures of an acute angle and an obtuse angle is 140. The sum of twice... (answered by MathLover1,josgarithmetic)

The sum of the measures an obtuse angle & an acute angle is 160 . the sum of the... (answered by jrfrunner)