a). The value of x for the Isosceles triangle is equal to 2
b). The value of x for the rectangle is equal to 2½
c). The measure of c for the angles on the straight line is 50°.
How to evaluate for the unknown values?
a). The figure is an Isosceles triangle which implies its two sides are equal so given the perimeter of 28cm we have that;
8 + 2(4x + 2) = 28
8 + 8x + 4 = 28 {open bracket}
12 + 8x = 28
8x = 28 - 12 {collect like terms}
8x = 16
x = 16/8 {divide through by 8}
x = 2
b). The rectangle has the length of its opposite side to be equal, so we solve for x as follows:
4x + 2 = 2x + 7
4x - 2x = 7 - 2 {collect like terms}
2x = 5
x = 5/2
x = 2½
c). The sum of angles on a straight line is equal to 180°, thus the measure of c is calculated as follows:
c + c + 80 = 180
2c + 80 = 180
2c = 180 - 80
2c = 100
c = 100/2
c = 50
In conclusion, tge value of x for the Isosceles triangle is 2, the value of x for the rectangle is equal to 2½ and the measure of c for the angles on the straight line is 50°.