The angles of a cyclic quadrilateral ABCD are
∠A = (6x + 10)°, ∠B = (5x)°
∠C = (x + y)°, ∠D = (3y – 10)°
Find x and y, and hence the values of the four angles.

NCERT Class X
Mathematics - Exemplar Problems

Chapter _PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

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Answers

2015-06-09T20:06:14+05:30

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According to the problem,

6x + 10 + x + y = 180
or, 7x + y = 170
or, y = 170 - 7x

Again, 5x + 3y - 10 = 180
or, 5x + 3y = 190
or, 5x + 3(170-7x) = 190
or, 5x + 510 - 21x = 190
or, -16x = -320
or, x = 20
So, y = 170 - 7x = 170 - 140 = 30

So, measure of all angles are 130°, 100°, 50°, 80°
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