Given rhombus RSTU, m∠T = 148⁰. What is m∠RSU?
if anyone can help me solve this and give me steps to solve these same questions in the future. would be much appreciated
To find the measure of angle RSU in rhombus RSTU, we can use the properties of a rhombus:
1. In a rhombus, opposite angles are equal. This means that angle RST is also 148°.
2. The sum of the angles in any quadrilateral (including a rhombus) is always 360°.
3. In a rhombus, adjacent angles are supplementary, meaning their measures add up to 180°.
Now, let's use these properties to find angle RSU:
1. Since angle RST is 148°, and opposite angles are equal, angle TSU is also 148°.
2. The sum of angle RST, angle TSU, angle TSU (opposite angle of RST), and angle RSU is equal to 360°.
3. Therefore, we can write an equation: 148° + 148° + 148° + angle RSU = 360°.
4. Simplifying the equation, we have: 444° + angle RSU = 360°.
5. Now, isolate the angle RSU by subtracting 444° from both sides of the equation: angle RSU = 360° - 444°.
6. Evaluating the right side of the equation, we have: angle RSU = -84°.
Since angles cannot have negative measures, we can conclude that angle RSU does not exist in the given rhombus.
In summary:
- In a rhombus, opposite angles are equal.
- The sum of the angles in any quadrilateral is always 360°.
- In a rhombus, adjacent angles are supplementary, adding up to 180°.
- To find the measure of an angle in a rhombus, you can use these properties and solve an equation.
m∠S = 180-148 = 32⁰
SU bisects angle S, so ...