quadrilateral abcd is inscribed in a circle.

what is the measure of angle a?

enter your answer in the box.

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.

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.

➷ Opposite angles in a cyclic quadrilateral equal 180 degrees

Therefore:

2x + 9 + 3x + 1 = 180

Simplify:

5x + 10 = 180

Subtract 10:

5x = 170

x = 34

2(35) + 9 = 77

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