Final answer:
To find the value of x, set the expression for m\(angle G) (2x + 33) equal to m\(angle H) (143°) and solve for x. The result is x = 55.
Step-by-step explanation:
The student has presented a problem involving congruent figures ARST and AFGH, and angle measurements that are given as expressions with variables. According to the given information, m\(angle ZH) is 143°, m\(angle R) is 18°, and m\(angle G) is given as 2x + 33. Since the figures ARST and AFGH are congruent, corresponding angles are equal. Therefore, m\(angle G) should be equal to m\(angle H) because they are corresponding angles in congruent figures. We already know that m\(angle H) is 143°, so we can set up the equation:
2x + 33 = 143
To solve for x, we subtract 33 from both sides:
2x = 143 - 33
2x = 110
Now, divide both sides by 2:
x = 55
So the value of x is 55.