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If opposite angles of a parallelogram are (3 x - 5)° and (51 - X)° find the measure of each angle.?
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If opposite angles of a parallelogram are (3 x - 5)° and (51 - X)° fin...
To solve for the angles of the parallelogram given the opposite angles as (3x - 5)° and (51 - x)°, we can use the property that opposite angles in a parallelogram are equal. Thus, we have the equation:
b Angles Equality
- (3x - 5) = (51 - x)
b Solving for x
1. Start by rearranging the equation:
- Add x to both sides:
(3x + x) - 5 = 51
- This simplifies to:
4x - 5 = 51
2. Next, add 5 to both sides:
- 4x = 56
3. Now, divide by 4:
- x = 14
b Finding the Angles
Now that we have the value of x, we can substitute it back into the expressions for the angles.
1. Calculate the first angle:
- Angle 1 = 3(14) - 5
- Angle 1 = 42 - 5 = 37°
2. Calculate the second angle:
- Angle 2 = 51 - 14
- Angle 2 = 37°
b Conclusion
- Since opposite angles are equal:
- The measure of each angle in the parallelogram is:
- Angle 1: 37°
- Angle 2: 143° (180° - 37°)
- Therefore, the angles of the parallelogram are:
- 37° and 143°.
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If opposite angles of a parallelogram are (3 x - 5)° and (51 - X)° find the measure of each angle.?
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