Question

Can someone please help me??? Its urgent. 15 Points.

Answer 1

Answer:

180 + x

Step-by-step explanation:

Answer 2

Answer:

The measure of arc ABC is 180 + x ⇒ 1st answer

Step-by-step explanation:

Let us revise some notes about the arcs of a circle

• The measure of an inscribed angle is half the measure of its subtended arc
• The measure of the central angle is equal to the measure of its subtended arc
• If two tangents intersect outside a circle then the measure of the angle formed between them is one-half the positive difference of the measures of the intercepted arcs

∵ CD and AD are two tangents to the given circle

∵ They intersected at point D out side the circle

∵ The measure of ∠ADC = x°

- By using the 3rd note above

∵ The intercepted arcs are arc ABC and arc AC

∴ x° = $\frac{1}{2}$ (measure of arc ABC - measure of arc AC)

- Multiply both sides by 2

∴ 2 x = (measure of arc ABC - measure of arc AC)

- Add measure of arc AC in both sides

∴ 2 x + measure of arc AC = measure of arc ABC ⇒ (1)

∵ The measure of a circle is 360°

∵ The arcs ARC and AC is formed the circle

∴ Measure of arc ABC + measure of arc AC = 360°

- Subtract measure of arc ABC from both sides

∵ Measure of arc AC = 360 - measure of arc ABC ⇒ (2)

- Substitute (2) in (1)

∴ 2 x + 360 - measure of arc ABC = measure of arc ABC

- Add measure of arc ABC to both sides

∴ 2 x + 360 = 2 measure of arc ABC

- Divide both sides by 2

∴ x + 180 = measure of arc ABC

∴ The measure of arc ABC is 180 + x