find the measure of each angle of an isosceles trapezoid if two of the angles has measures in the ratio of 2:3.
the sum of the 4 angles is 360°
But they come in equal pairs.
let the larger be 3x and the smaller be 2x
3x + 2x = 180
x = 36
so the angles are 72° and 108°
check: 72:108 = 2:3
72+72+108+108 = 360
thank you reiny
Hi thank you for the answer❣️
Thank you
Well, aren't angles a funny thing? Let's unravel this angle-twister!
We know that an isosceles trapezoid has two parallel sides (the bases) and two congruent angles.
Let's call the first angle "2x" and the second angle "3x." Now, since the angles in a trapezoid add up to 360 degrees, we can set up an equation:
2x + 3x + 2x + 3x = 360
Simplifying this equation, we have:
10x = 360
Dividing both sides by 10, we get:
x = 36
Now let's find the measures of the angles:
Angle 1: 2x = 2(36) = 72 degrees
Angle 2: 3x = 3(36) = 108 degrees
Since the trapezoid has two congruent angles, the other two angles must also measure 72 and 108 degrees.
And there you have it—the measure of each angle in your isosceles trapezoid! Keep the geometry laughs coming!
To find the measure of each angle in an isosceles trapezoid, we need to understand a few things.
1. The opposite angles of an isosceles trapezoid are equal in measure.
2. The sum of all four angles in any quadrilateral is 360 degrees.
Let's assign variables to the angles:
Let one of the angles have a measure of 2x.
And let the other angle have a measure of 3x.
Now, we can set up an equation using the information given:
2x + 3x + 2x + 3x = 360
Combine like terms:
10x = 360
Divide both sides by 10:
x = 36
Now, substitute x back into our angle measures:
Angle 1 = 2x = 2(36) = 72 degrees
Angle 2 = 3x = 3(36) = 108 degrees
Therefore, the measure of each angle in the isosceles trapezoid is 72 degrees, 108 degrees, 72 degrees, and 108 degrees.