Angle C is an inscribed angle of circle P. Angle C measures (-3x - 6)° and arc AB measures (-4x)° . Find x.

circle P with points A, B, and C on the circle and inscribed angle A C B drawn
Question 4 answers

-2

-4

-6

-8

Something is not right here.

You say arc AB = -4x °, but the arc AB would not be measured in degrees.
Did you mean the central angle subtended by arc AB is -4x° ? That would make sense.

If so, then the central angle subtended by an arc is twice the angle subtended by the same arc at the circle.
then
-4x = 2(-3x - 6)
-4x = -6x - 12
2x = -12
x = -6 , which is one of the choices

B = 4x + 10

2.5

Angle C is an inscribed angle of circle P. Angle C measures (3x + 5)° and arc AB measures (16x)°. Find x.

Imported Asset


1

5

3

9

To solve for x, we can use the relationship between inscribed angles and their corresponding arcs. In a circle, an inscribed angle is equal to half of its intercepted arc.

Given that angle C measures (-3x - 6)° and arc AB measures (-4x)°, we can set up the following equation:

(-3x - 6)° = 1/2 * (-4x)°

To solve for x, we need to isolate x. Let's simplify the equation step by step:

(-3x - 6)° = 1/2 * (-4x)°
Multiply both sides by 2 to eliminate the fraction:
-6x - 12 = -4x

Now, let's group the x terms:
-6x + 4x = -12

Combine like terms:
-2x = -12

Divide both sides by -2:
x = 6

Therefore, the value of x is 6.