Question

What is the measure of AC ? Enter your answer in the box. °

Answer 1

Answer: $33^{\circ}$

Step-by-step explanation:

We know that, the inscribed angle theorem says that the measure of an inscribed angle is exactly half the measure of its intercepted arc.

In the given picture , the inscribed angle = (2.5x+4)°

The intercepted arc = (7x-2)°

Then by inscribed angle theorem , we have

$(2.5x+4)=\dfrac{1}{2}\times (7x-2)\\\\\Rightarrow\ 2(2.5x+4)=7x-2\\\\\Rightarrow\ 5x+8=7x-2\\\\\Rightarrow\ 7x-5x=8+2\\\\\Rightarrow\ 2x=10\\\\\Rightarrow\ x=\dfrac{10}{2}=5$

Now, the measure of $\overarc{AC}=(7x-2)^{\circ}=(7(5)-2)^{\circ}=(35-2)^{\circ}$

$=33^{\circ}$

Hence, the measure of arc AC $=33^{\circ}$

Answer 2

Solution:

we are given that

Inscribed angle$=(2.5x+4)$

Intercepted arc$=(7x-2)$

As we know that the Inscribed angle is Half of the measure of the intercepted arc.

So we can write

$(2.5x+4)=\frac{1}{2}(7x-2) \\\\7x-2=2(2.5x+4)\\\\7x-2=5x+8\\\\7x-5x=8+2\\\\2x=10\\\\x=5\\\\\text{So Measure of arc AC}=(7x-2)=7*5-2=35-2=33$