Question
If the measure of arc AC is 76^circ and the mangle ABC=2x-12 what is the value of x? x=25 x=13 x=44 x=38
Answer
4.1
(167 Votes)
Nessa
Elite · Tutor for 8 years
Answer
# ExplanationTo solve for
in the given problem, we need to understand the relationship between the measure of the arc
and the angle
.In a circle, the measure of an inscribed angle is half the measure of the intercepted arc. Therefore, if
intercepts arc
, then:
Given:- The measure of arc
is
.-
.Using the relationship between the inscribed angle and the intercepted arc, we have:
Since
, we can set up the equation:
To solve for
, follow these steps:1. Add 12 to both sides of the equation:
2. Divide both sides by 2:
Therefore, the value of
is 25.# Answer