Question

find the value of x.
x =

Explanation:

Step1: Note angle - sum relationship

We know that the sum of angles around a point is 360°. Here, considering the right - angle (90°), the 56° angle, the 79° angle and the (2x + 5)° angle, we can set up an equation. Since the non - overlapping angles at point F form a full - circle (360°) and we are dealing with a right - angled situation, we can also consider the sum of the non - right angles. The sum of the angles ∠AFB, ∠BFC and ∠CFD is 180° (a straight - line angle). So, 56°+79°+(2x + 5)°=180°.

Step2: Simplify the left - hand side of the equation

First, combine the constant terms on the left - hand side: 56+79 + 5=140. The equation becomes 140+2x=180.

Step3: Solve for x

Subtract 140 from both sides of the equation: 2x=180 - 140. So, 2x = 40. Then divide both sides by 2: x = 20.

Answer:

20