Find the angles of a parallelogram if it is known that one of them is 50° greater than the other

Let the angles of the parallelogram be \( x \) and \( x + 50^\circ \).

Since the sum of the adjacent angles in a parallelogram is always \( 180^\circ \), we can set up the equation:

\[
x + (x + 50^\circ) = 180^\circ
\]

Solving this:

\[
2x + 50^\circ = 180^\circ
\]
\[
2x = 180^\circ - 50^\circ
\]
\[
2x = 130^\circ
\]
\[
x = 65^\circ
\]

Thus, one angle is \( 65^\circ \) and the other angle is:

\[
x + 50^\circ = 65^\circ + 50^\circ = 115^\circ
\]

Since a parallelogram has two pairs of equal opposite angles, the angles of the parallelogram are:

\[
65^\circ, 115^\circ, 65^\circ, 115^\circ
\]

### Summary:
The angles of the parallelogram are **65° and 115°**.

Would you like further details, or do you have any questions?

Here are five related questions to deepen your understanding:
1. How do we know that the sum of adjacent angles in a parallelogram is always 180°?
2. Can a parallelogram have all angles equal? If yes, what shape does it form?
3. If one angle of a parallelogram is 120°, what are the measures of the other three angles?
4. How do you calculate the angles of a parallelogram if you know the measure of one angle?
5. What other properties of a parallelogram are important in geometry?

**Tip:** In any quadrilateral, the sum of all angles is always 360°, which helps in solving for unknown angles.

Find the angles of a parallelogram if it is known that one of them is 50° greater than the other.

Learn how to find the angles of a parallelogram when one angle is 50° greater than the other. The solution includes step-by-step algebraic work and uses key geometric theorems. This problem is suitable for students in Grades 7-9.

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