Question

​ Quadrilateral ABCD ​ is inscribed in a circle.

What is the measure of angle A?



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m∠A=

°

A quadrilateral inscribed in a circle. The vertices of quadrilateral lie on the edge of the circle and are labeled as A, B, C, D. The interior angle A is labeled as left parenthesis 2 x plus 9 right parenthesis degrees. The angle C is labeled as left parenthesis 3 x plus 1 right parenthesis degrees.

Answer 1

The opposite angles in a quadrilateral need to equal 180 degrees.

This means the sum of angle A and angle C need to equal 180.

(2x+9) + (3x+1) = 180

Simplify the left side:

5x + 10 = 180

Subtract 10 from each sode:

5x = 170

Divide both sides by 5:

x = 170 / 5

x = 34

Now you have the value for x, use this to find angle A.

A = 2x +9 = 2(34) + 9 = 68 + 9 = 77 degrees.

Answer 2

The measure of angle A is 77 degree.

What is a Quadrilateral?

A Quadrilateral is a polygon with four sides.

When a quadrilateral is inscribed in a circle, the sum of the opposite sides is equal to 180 degree.

m∠A + m∠C = 180

2x+9 +3x+1 =180

5x +10 =180

5x =170

x = 34

m∠A = 2 * 34 +9

m∠A =77 degree

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