Question

what is the value of x?
there is a circle with center d. there are three red angles at the center: x+91°, x+16°, x+82°, and the fourth angle (between e and f) is not labeled with an expression. the question is to find the value of x. there is a box to enter the value of x and a submit button. also, there are some help links at the bottom: work it out, not feeling ready yet? these can help:, and some topics like solve linear equations: mixed review, angle measures.

Explanation:

Step1: Sum of angles in a circle

The sum of angles around a point (in a circle) is \(360^{\circ}\). So, \((x + 91)+(x + 16)+(x + 82)=360\).

Step2: Simplify the left - hand side

Combine like terms: \(3x+91 + 16+82=360\), which simplifies to \(3x+189 = 360\).

Step3: Solve for \(x\)

Subtract \(189\) from both sides: \(3x=360 - 189\), so \(3x = 171\). Then divide both sides by \(3\): \(x=\frac{171}{3}\).

Answer:

\(x = 57\)