Question

question 3 not yet answered marked out of 2.00 flag question which statement about the angles in this diagram is false? select one: a. <f = 62° b. <e = 130° c. <c = 50° d. <b = 50°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle \(f\) and the \(62^{\circ}\) angle are vertical angles, so \(\angle f=62^{\circ}\), option a is true.

Step2: Use vertical - angle property

Angle \(e\) and the \(130^{\circ}\) angle are vertical angles, so \(\angle e = 130^{\circ}\), option b is true.

Step3: Use supplementary - angle property

\(\angle c\) and the \(130^{\circ}\) angle are supplementary (linear - pair). Since \(130^{\circ}+\angle c=180^{\circ}\), then \(\angle c=180^{\circ}- 130^{\circ}=50^{\circ}\), option c is true.

Step4: Use angle - relationship in triangle

\(\angle b\) and the \(130^{\circ}\) angle are not supplementary in the way assumed in option d. In fact, \(\angle b\) and \(\angle c\) are vertical angles, so \(\angle b = 50^{\circ}\) is false because \(\angle b\) and the \(130^{\circ}\) angle are not related as such in the given diagram.

Answer:

d. \(\angle b = 50^{\circ}\)