Find the measures of <1 and <2. Be sure to justify your answer with either work or an explanation. The shape is a trapezoid. Base: 110 degrees, Base angle 1: 2, Base angle 2: 1
show work.
Since the sum of the angles in a trapezoid is 360 degrees, we can begin by using the formula:
sum of angles = (n - 2) x 180
where n is the number of sides. For a trapezoid, n = 4, so we have:
sum of angles = (4 - 2) x 180
sum of angles = 2 x 180
sum of angles = 360
We know that one of the angles is 110 degrees, so we can subtract that from the sum to find the total of the other three angles:
360 - 110 = 250
Now we can set up an equation to solve for the measures of angles 1 and 2:
2x + x + 110 = 250
Combining like terms, we get:
3x + 110 = 250
Subtracting 110 from both sides, we get:
3x = 140
Dividing by 3, we get:
x = 46.67
So angle 1 is:
2x = 93.33 degrees
And angle 2 is:
x = 46.67 degrees
So the measures of angles 1 and 2 are 93.33 degrees and 46.67 degrees, respectively.