The measures of the acute angles in the isosceles trapezoid are "one-half times the measures of the obtuse angles". write and solve a system of equations to find the measures of all the angles.

The measure of acute angles is 60° and measure of obtuse angles is 120°

Step-by-step explanation: A trapezoid 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 180°.

The measures of the acute angles in the isosceles trapezoid are "one-half times the measures of the obtuse angles".

Let us assume the measure of obtuse angles = x°.

And measure of acute angles = y°

Sum of an acute angle and an obtuse angle is 180°.

Therefore,

x+y =180 (1)

Also,

y = 1/2 x  (2).

Substituting y= 1/2x in first equation we get

x+ 1/2 x = 180.

3/2 x = 180.

Multiplying both sides by 2, we get

2× 3/2x = 2×180

3x = 360

Dividing both side by 3, we get

3x/3 = 360/3

x= 120.

Plugging value of x in second equation, we get

y= 1/2x = 1/2(120) =60.

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