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.