Questions: Quadrilateral GVWX is a rhombus, What is mLTUY?

Transcript text: Quadrinteral $G V W X$ is a mombus, What is mLTUY?

Solution

Solution Steps

Step 1: Properties of a rhombus

A rhombus is a parallelogram with all four sides equal in length. Its diagonals are perpendicular bisectors of each other. This means the diagonals intersect at a right angle and divide each other into two equal parts.

Step 2: Analyze the given information

We are given that quadrilateral UVWX is a rhombus, and that the measure of angle UXV is 55°. We are asked to find the measure of angle TUV.

Step 3: Determine the measure of angle UXV

Since the diagonals of a rhombus bisect the angles, angle UXW is twice the measure of angle UXV. Therefore, angle UXW = 2 * 55° = 110°.

Step 4: Determine the measure of angle XUW

The sum of the angles in a triangle is 180°. In triangle UXW, we have: angle UXW + angle XUW + angle XWU = 180° Since UVWX is a rhombus, angle XWU is equal to angle UXW. So, 110° + angle XUW + 110° = 180° 220° + angle XUW = 180° angle XUW = 180° - 220° This is not possible.

Step 5: Consider the diagonals

Since the diagonals of a rhombus are perpendicular bisectors, angle UTV is 90°. In triangle UXV, angle UXV is given as 55°. Therefore, angle XUV = 180° - 90° - 55° = 35°. Since the diagonals bisect the angles, angle TUV is equal to angle XUV. Therefore, angle TUV = 35°.

Final Answer

\$\boxed{m\angle TUV = 35^\circ}\$

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