Question

The figure below shows a triangle with vertices A and B on a circle and vertex C outside it. Side AC is tangent to the circle. Side BC is a secant intersecting the circle at point X:
What is the measure of angle ACB?

Answer 1

Answer:

32

Step-by-step explanation:

First, one theorem states that (arc AB - arc AX) / 2 = angle ACB. We know that arc AB is 176, so we have

(176 - arc AX) /2 = ∠ACB

Next, the Inscribed Angle Theorem states that

arc AX/2 = ∠ABX

multiply both sides by 2

56 * 2 = arc AX = 112

Therefore, ∠ACB = (176-112)/2 = 64/2 = 32

Answer 2

The figure below shows a triangle with vertices A and B on a circle and vertex C outside it. the measure of angle ACB is 32.

What is the circle theorem?

One of the theorems of a circle states that the angles in the same segments or on the same chord are equal.

First, one theorem states that (arc AB - arc AX) / 2 = angle ACB.

The figure below shows a triangle with vertices A and B on a circle and vertex C outside it.

Side AC is tangent to the circle.  Side BC is a secant intersecting the circle at point X

We know that arc AB is 176,

(176 - arc AX) /2 = ∠ACB

Next, the Inscribed Angle Theorem states that

arc AX/2 = ∠ABX

multiply both sides by 2

56 x 2 = arc AX

= 112

Therefore, ∠ACB = (176-112)/2

                        = 64/2 = 32

Learn more about theorem of circle;

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