Question

7 the figure shows a triangle with an angle bisector. find the measure of \\( \angle f d e \\) if \\( \angle 1 = 28 ^ { \circ } \\).

1. the figure shows a triangle with an angle bisector. if \\( \angle 1 = 2 x - 6 \\) and \\( \angle 2 = x + 4 \\). find \\( x \\).

Explanation:

Question 7

Step1: Use the definition of angle bisector

An angle bisector divides an angle into two equal parts. So, \(\angle 1=\angle 2\).

Step2: Calculate \(\angle FDE\)

Since \(\angle FDE=\angle 1 + \angle 2\) and \(\angle 1 = 28^{\circ}\), \(\angle 2=28^{\circ}\), then \(\angle FDE=28^{\circ}+28^{\circ}\)

Step1: Use the property of angle bisector

Because of the angle - bisector, \(\angle 1=\angle 2\). Given \(\angle 1 = 2x-6\) and \(\angle 2=x + 4\), we set up the equation \(2x-6=x + 4\)

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(2x-x-6=x-x + 4\), which gives \(x-6=4\). Then add 6 to both sides: \(x-6 + 6=4+6\)

Answer:

\(56^{\circ}\), so the answer is A.

Question 8