Question

what is the value of x? h 92° e g f x + 61° x = °

Explanation:

Step1: Recall cyclic - quadrilateral property

In a cyclic quadrilateral, the sum of opposite angles is 180°. Angles ∠H and ∠F are opposite angles in the cyclic quadrilateral EFGH.

Step2: Set up the equation

We know that ∠H+∠F = 180°. Given ∠H = 92° and ∠F=x + 61°. So, 92+(x + 61)=180.

Step3: Simplify the equation

First, combine like - terms: 92+61+x=180, which gives 153+x=180.

Step4: Solve for x

Subtract 153 from both sides of the equation: x=180 - 153.
x = 27

Answer:

27