solve this---**Question Number:** 14
**Image Description:**
* **Type:** Geometric figure (Quadrilateral).
* **Main Elements:**
* A four-sided polygon with vertices labeled A, B, C, and D in counterclockwise order starting from the bottom left.
* Angle at vertex A is labeled as 45°.
* Angle at vertex B is labeled as x°.
* Angle at vertex C is labeled as x°.
* Angle at vertex D is labeled as x°.
**Question Stem:**
In the figure above, what is the value of x?
**Options:**
A) 45
B) 90
C) 100
D) 105
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In this problem, we have a quadrilateral ABCD. We're given that angle A is 45 degrees, and the other three angles B, C, and D all equal x degrees. Our task is to find the value of x. Let's start by recalling what we know about the sum of interior angles in a quadrilateral.
To solve this problem, we'll use the fact that the sum of interior angles in any quadrilateral is 360 degrees. We have one angle of 45 degrees and three angles each equal to x degrees. Setting up the equation: 45 degrees plus x degrees plus x degrees plus x degrees equals 360 degrees. Simplifying: 45 degrees plus 3x degrees equals 360 degrees. Solving for x: 3x degrees equals 315 degrees, which means x equals 105 degrees. Therefore, the value of x is 105 degrees, which corresponds to option D.
To solve this problem, we'll use the fact that the sum of interior angles in any quadrilateral is 360 degrees. We have one angle of 45 degrees and three angles each equal to x degrees. Setting up the equation: 45 degrees plus x degrees plus x degrees plus x degrees equals 360 degrees. Simplifying: 45 degrees plus 3x degrees equals 360 degrees. Solving for x: 3x degrees equals 315 degrees, which means x equals 105 degrees. Therefore, the value of x is 105 degrees, which corresponds to option D.
We have found that the value of x is 105 degrees. Looking at our multiple choice options, the correct answer is D, which is 105. To summarize our solution: First, we used the fact that the sum of interior angles in any quadrilateral is 360 degrees. Then, we set up the equation 45 degrees plus 3x degrees equals 360 degrees. Finally, we solved for x to get 105 degrees. This problem demonstrates how to apply the properties of quadrilaterals to find unknown angle measures.