Question

If STUV is a rectangle and m/VSU = 52°, what is the value of x? A. 104 B. 52, C. 38 D. 98 E. 64 F. Cannot be determined

Answer 1

To determine the value of x, we must understand whether the question refers to the interior angle adjoining VSU or the exterior angle at S in rectangle STUV. If the question aims at the interior angle, none of the options match, but if it refers to the exterior angle at S, then the answer is B. 52.

Step-by-step explanation:

The question asks us to find the value of x given that STUV is a rectangle and the measure of angle VSU is 52°. In a rectangle, adjacent angles are supplementary, meaning that they add up to 180°. Since VSU is one of these angles, the adjacent angle U (or x) will also be 180° - 52° = 128°. However, this value does not match any of the provided options. Thus, if the question is asking for the measure of angle U, none of the listed options match, possibly indicating a typo or mistake in the question or the options given.

If the question is asking for the exterior angle formed by extending one side of the rectangle beyond point S, the value of x would indeed be 52° because exterior angles of rectangles are congruent to their corresponding interior angles. In this case, the answer would be B. 52, aligning with the measure of angle VSU. Without additional context or a diagram, the answer F.

Answer 2

To find the value of x in the rectangle STUV, we can subtract the given angles from 180° to find the measure of angle VUT. Since opposite angles in a rectangle are equal, angle VUT is equal to angle VST. Therefore, the value of x is 52°.

Step-by-step explanation:

To find the value of x, we need to use the fact that STUV is a rectangle, which means that opposite angles are equal. Since m/VSU is given as 52°, that means m/VUT is also 52°. Since the sum of the angles in a triangle is 180°, we can find the measure of angle VUT by subtracting the given angles from 180°. So, angle VUT = 180° - 52° - 52° = 76°. Since opposite angles in a rectangle are equal, angle VUT is equal to angle VST.

So, x = 52°.