Question

Inscribed angles math lib Need help with 5, 6, 7, 8 thank you !!!

Answer 1

Answer:

5. B) x = 7

6. D) 35°

7. C) 67°

8. A) 142°

Step-by-step explanation:

5. Inscribed angle of a semicircle is equal to 90°. Therefore,

16x - 22 = 90

Solve for x

16x - 22 + 22 = 90 + 22

16x = 112

16x/16 = 112/16

x = 7

6. Recall: inscribed angle = ½(intercepted arc)

3x - 1 = ½(8x - 26)

2(3x - 1) = 8x - 26

6x - 2 = 8x - 26

Collect like terms

6x - 8x = 2 - 26

-2x = -24

-2x/-2 = -24/-2

x = 12

m<LMN = 3x - 1

Plug in the value of x

m<LMN = 3(12) - 1 = 36 - 1

m<LMN = 35°

7. Recall: inscribed angle = ½(intercepted arc)

Therefore,

4x + 28 = ½(11x - 1)

2(4x + 28) = 11x - 1

8x + 56 = 11x - 1

Collect like terms

8x - 11x = -56 - 1

-3x = -57

-3x/-3 = -57/-3

x = 19

Arc BC = 360° - (Arc AC + Arc AB) (Full circle)

Substitute

Arc BC = 360 - (11x - 1 + 85)

Plug in the value of x

Arc BC = 360 - (11*19 - 1 + 85)

Arc BC = 360 - (209 - 1 + 85)

Arc BC = 360 - 293

Arc BC = 67°

8. Inscribed angles intercepted by the same arc are equal. Therefore,

8x - 41 = 5x + 1

Collect like terms

8x - 5x = 41 + 1

3x = 42

3x/3 = 42/3

x = 14

5x + 1 = ½(arc PS) => inscribed angle = ½ of intercepted arc

2(5x + 1) = arc PS

Plug in the value of x

2(5*14 + 1) = arc PS

2(70 + 1) = arc PS

2(71) = Arc PS

Arc PS = 142°