Question

Multi-Step Find the angle measures of each inscribed quadrilateral.
10-13 20 points please help

Answer 1

The angle measure of each inscribed quadrilateral is as follows;

10

∠P = 90°

∠R = 90°

∠Q = 140°

∠S = 40°

11.

∠A = 70°

∠C = 110°

∠ B  = 115°

∠D = 55°

12.

∠B = 100°

∠D = 80°

∠E = 141°

∠C = 39°

13.

∠V = 101°

∠T  = 79°

∠U = 86°

∠W = 94°

Cyclic Quadrilateral

A cyclic quadrilateral has all it vertices on the circumferences of the circle .   opposite angle of a cyclic quadrilateral add up to 180 degrees. The sum of the whole angles add up to 360 degrees. Therefore, tha angle measure of each inscribed quadrilateral is as follows

10.

5x + 20 + 7x - 8 = 180

12x + 12 = 180

12x = 180 - 12

12x = 168

x = 168 / 12

x = 14

Therefore,

• ∠P = 5x + 20 = 5(14) + 20 = 90°
• ∠R = 90°
• ∠Q = 10x = 10(14) = 140°
• ∠S = 40°

11.

4z - 10 + 10 + 5z = 180

9z = 180

z = 20

Therefore,

• ∠A = 4z - 10 = 4(20) - 10 = 70°
• ∠C = 110°
• ∠ B = 6z - 5  = 6(20) - 5 = 115°
• ∠D = 55°

12.

1 / 2 z + 1 / 4 z + 30 = 180

3 / 4 z + 30 = 180

3 / 4 z = 150

3z = 600

z = 600 / 3

z = 200

Therefore,

• ∠B = z / 2 = 200 / 2 = 100°
• ∠D = z / 4 + 30 = 200 / 4 + 30 = 80°
• ∠E = z - 59 = 200 - 59 = 141°
• ∠C = 39°

13.

15y - 4 + 12y - 5 = 180

27y = 180 + 9

y = 189 / 27

y = 7

14 + 4x + 6x - 14 = 180

10x = 180

x = 18

Therefore,

• ∠V = 15y  - 4 = = 101°
• ∠T  = 79°
• ∠U = 14 + 4x= 14 + 72= 86°
• ∠W = 94°

learn more on quadrilateral here: https://brainly.com/question/9177423