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 4 x plus 5 right parenthesis degrees. The angle C is labeled as left parenthesis x plus 15 right parenthesis degrees.

Step-by-step explanation:

The opposite angles of any quadrilateral that is inscribed in a circle are supplementary. This means that the opposite angles add up to give 180°.

m∠A is supplementary to m∠C. Therefore,

4x + 5 + x + 15 = 180

Collecting like terms, it becomes

4x + x + 15 + 5 = 180

5x + 20 = 180

Subtracting 20 from the Left hand side and the right hand side of the equation, it becomes

5x + 20 - 20 = 180 - 20

5x = 160

Dividing the Left hand side and the right hand side of the equation by 5, it becomes

5x/5 = 160/5

x = 32

Therefore,

m∠A = (4 × 32) + 5

m∠A = 133°

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.