Question

In a quadrilateral abcd, angle a=72 and angle c is the supplementary of angle
a. the other two angles are 2x-10 and x+4. find the value of x and measure of all the angles

Answer 1

a+c=180
72+c=180
c=180-72
c=108.
If opposite angles are supplementary,then the quadrilateral is cyclic.
$2x - 10 + x + 4 = 180 \\ 3x - 6 = 180 \\ 3x = 186 \\ x = \frac{186}{3} \\ x = 62 \\ 2x - 10 \\ 2 \times 62 - 10 \\ 124 - 10 \\ 114 \\ x + 4 \\ 62 + 4 \\ 66$
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