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The diagram shows a kite with vertices \( V \), \( U \), \( S \), and \( T \). In a kite, the adjacent sides are congruent, meaning that \( UV = VS \) and \( UT = ST \), as indicated by the tick marks on the sides. We are tasked with finding the measure of \( \angle T \).

The two pairs of congruent sides lead to the following side lengths:

- \( UT = ST = 14x \)
- \( US = 12x - 5 \)

Since the quadrilateral is a kite, the diagonals intersect at right angles. The angle we are asked to find is \( \angle T \), which is formed at the bottom vertex of the kite.

To proceed:
1. Use the equality of the two diagonal lengths to solve for \( x \) by setting the two expressions for the sides equal to each other (since the diagonals are perpendicular bisectors, this will help solve for \( x \)).
2. Once \( x \) is found, use trigonometric or geometric reasoning based on the properties of kites to determine the measure of \( \angle T \).

Let me calculate that for you.The solution for \( x \) is \( -\frac{5}{2} \). Since a side length cannot be negative, this implies there's an error in the setup or the given side lengths.

Let me recheck the approach and clarify the next step based on the properties of the kite to find the measure of \( \angle T \).

Find the measure of angle T in a kite with side lengths UT = 14x, US = 12x - 5, and given kite properties.

Solve the problem of finding the measure of angle T in a kite using algebraic expressions for side lengths and kite properties. Learn how to apply the Kite Diagonals Theorem and use congruence to calculate angle measures. Suitable for students in Grades 9-10.

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