Question

2
In the figure, ABCD is a cyclic quadrilateral, CBQ=51"
and a = 2b find the value of b.
​

Answer 1

The value of b is 39°

Explanation:

Given that ABCD is a cyclic quadrilateral.

The measure of $\angle CBQ=51^{\circ}$ and $a=2b$

We need to find the value of b

By angle sum property, all the angles in a triangle add upto 180°

Hence, using this property, we have,

$51^{\circ}+90^{\circ}+b=180^{\circ}$

Adding the values, we get,

$141^{\circ}+b=180^{\circ}$

Subtracting both sides by 141, we have,

$b=180^{\circ}-141^{\circ}$

Simplifying, we get,

$b=39^{\circ}$

Hence, the value of b is 39°

Substituting b=39° in $a=2b$, we have,

$a=2(39)$

$a=78^{\circ}$

Thus, the value of a is 78°

Hence, the value of a and b is 78° and 39°

Learn more:

(1) In the given fig. ABCD is a cyclic quadrilateral and O is the centre of circle. If angle CBQ = 60°and x = 2y, find the valies of x, y and z. Also find angle AOC.

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(2) Abcd is a cyclic quadrilateral such that angle a (4y+20) angle b=(3y-5) angle c=-4x and angle d=7x+5

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