Question

From the given figure, find out the values of a and b. when
A = (a + 9° ; B = (2a + 3)
C = (56 + 6)° and D=(45 – 3)º

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Answer 1

Answer:

a = 40°    b = 25°

Step-by-step explanation:

∠A = a + 9

∠B = 2a + 3

∠C = 5b + 6

∠D = 4b - 3

As it is a cyclic quadrilateral; ∠A + ∠C = 180° and ∠B + ∠D = 180°

∠A + ∠C = a + 9 + 5b + 6 = a + 5b + 15 = 180

⇒ a + 5b = 165                                                ----- eq1

B + D = 2a + 3 + 4b -3 = 2a +4b = 180

⇒ a + 2b = 90                                                 ----- eq2

eq1 - eq 2

⇒ 3b = 75

⇒ b = 25

from eq2

⇒ a + 2b = 90

⇒ a + 2(25) = 90

⇒ a = 40