Answer:
So for the triangle, we have x = 25 and the angles 45-75-60.
So for the quadrilateral, we have x = 75 and the angles 70-110-75-105.
Step-by-step explanation:
For each of these problems, we can simply add the expressions of the angles given matched to the sum of the angles for the shape given below. Once we do this, we can solve for x, and then state the given measures of each angle of the shapes.
<u>For the triangle:</u>
60 + ( x + 20 ) + 3x = 180
60 + x + 20 + 3x = 180
60 + 20 + x + 3x = 180
80 + x ( 1 + 3 ) = 180
80 + x ( 4 ) = 180
80 + 4x = 180
4x = 100
x = 25
We have the given angles:
x + 20 ==> 25 + 20 ==> 45
3x ==> 3 (25) ==> 75
60
So for the triangle, we have the angles 45-75-60.
<u>For the quadrilateral:</u>
( x - 5 ) + ( x + 35 ) + x + 1.4x = 360
x - 5 + x + 35 + x + 1.4x = 360
35 - 5 + x + x + x + 1.4x = 360
30 + x ( 1 + 1 + 1 + 1.4 ) = 360
30 + x ( 4.4 ) = 360
30 + 4.4x = 360
4.4x = 330
x = 75
So, we have the given angles:
x - 5 ==> 75 - 5 ==> 70
x + 35 ==> 75 + 35 ==> 110
x ==> 75
1.4x ==> 1.4(75) ==> 105
So for the quadrilateral, we have the angles 70-110-75-105.
Cheers.
