Respuesta :
Answer: 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.
