Question

PLSS GEOMETRY 50POINTS
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Answer 1

Answer: D 49

Explanation:

The 2 angles are the same because the lines extend out to the same arc.

10x-1 = 8x+9 >Solve for x

2x - 1 = 9

2x = 10

x = 5

<J = 10x - 1 >substitute x

<J = 10(5) - 1

<J = 50 - 1

<J = 49

Answer 2

D) 49°

Explanation:

According to Angle Subtended by the Same Arc Theorem, the angles at the circumference subtended by the same arc are equal.

Therefore, for the given circle, ∠J = ∠I.

First find the value of x by equating the expressions for angles J and I:

⇒ ∠J = ∠I

⇒ (10x - 1)° = (8x + 9)°

⇒ 10x - 1 = 8x + 9

⇒ 10x - 1 - 8x = 8x + 9 - 8x

⇒ 2x - 1 = 9

⇒ 2x - 1 + 1 = 9 + 1

⇒ 2x = 10

⇒ 2x/2 = 10/2

⇒ x = 5

To find the measure of angle J, substitute the found value of x into the expression for ∠J:

⇒ ∠J = (10x - 1)°

⇒ ∠J = (10(5) - 1)°

⇒ ∠J = (50 - 1)°

⇒ ∠J = 49°

Therefore, the measure of ∠J is 49°.