there exists a circle with chords. the chords are congruent. their corresponding arc measurements are 80 degrees and 2x+10 solve for x
2 x + 10 = 80
2 x = 70
x = 35
To solve this problem, we'll use the fact that congruent chords in a circle subtend congruent arcs.
Let's denote the measure of each chord as y degrees.
We know that the corresponding arc measurement for one of the chords is 80 degrees. This means that the measure of the arc subtended by the other chord is also 80 degrees.
Now, we can set up an equation based on the given information:
2x + 10 = 80
To solve for x, we will isolate the variable:
2x = 80 - 10
2x = 70
Dividing both sides of the equation by 2, we find:
x = 70/2
x = 35
Therefore, the solution to the equation is x = 35.
This means that the measure of the other chord is 2(35) + 10 = 80 degrees.