Question

in the figure below, what is the measure of the larger of the two angles? a 100° b 160° c 200° d 260°

Explanation:

Step1: Set up the equation

The sum of angles around a point is \(360^{\circ}\). So, \(x+(x + 160)=360\).

Step2: Solve for \(x\)

Combine like - terms: \(2x+160 = 360\).
Subtract \(160\) from both sides: \(2x=360 - 160\), \(2x = 200\).
Divide both sides by \(2\): \(x = 100\).

Step3: Find the larger angle

The two angles are \(x = 100^{\circ}\) and \(x + 160\). Substitute \(x = 100\) into \(x + 160\), we get \(100+160=260^{\circ}\).

Answer:

D. \(260^{\circ}\)