Question

angle abc is a straight angle. the measure of angle abd is 100°. the measure of angle dbc is x°. what is the value of x?

Explanation:

Step1: Recall the property of a straight angle

A straight angle measures \(180^{\circ}\). So, \(\angle ABC=180^{\circ}\).

Step2: Use the angle - addition postulate

Since \(\angle ABC=\angle ABD+\angle DBC\), and \(\angle ABD = 100^{\circ}\), \(\angle DBC=x^{\circ}\), we have the equation \(180 = 100+x\).

Step3: Solve the equation for \(x\)

Subtract \(100\) from both sides of the equation: \(x=180 - 100\).
So, \(x = 80\).

Answer:

\(x = 80\)