How to find an angle in a parallelogram - Math

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of degrees)--i.e. angles degrees.

Thus, the solution is:

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of degrees)--i.e. angles degrees.

Thus,

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of degrees).

Thus, the solution is:

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of degrees).

Thus, the solution is:

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of degrees)--i.e. angles degrees.

The solution to this problem is:

Therefore,

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of degrees)--i.e. angles degrees.

The solution to this problem is:

Thus,

A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of degrees).

Since, angle and are supplementary the solution is:

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of degrees).

The first step to solving this problem is to find the measurement of angle . Since angle is a supplementary angle to angle , angle

Since, angle and are opposite interior angles they must be equivalent.

Thus, the final solution is:

A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of degrees).

Since, angles and are opposite interior angles, they must be equivalent.

Therefore, the solution is:

A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of degrees).

Since, angles and are opposite interior angles, thus they must be equivalent.

, therefore

A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of degrees).

Thus, the solution is:

Since both angles and equal There sum must equal

A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees.

Also, the adjacent interior angles must be supplementary angles (sum of degrees).

Since, angles and are adjacent to each other they must be supplementary angles.

Thus, the sum of these two angles must equal degrees.

This question is very simple to answer if you remember that ALL paralellograms have two pairs of equal and opposite angles, and that the four angles in any quadrilateral MUST add up to 360 degrees.

Because the angles given are different, we know that they are supplementary and the other two missing angles MUST be the same.

The diagonals of a parallelogram are perpendicular - and, consequently, is a right angle. - if and only if the parallelogram is a rhombus, a figure with four sides of equal length. Not all rectangles have four congruent sides. Therefore, need not be a right angle.

Below is regular Pentagon with center , a segment drawn from to each vertex - that is, each of its radii drawn.

The measure of each angle of a regular pentagon can be calculated by setting equal to 5 in the formula

and evaluating:

Specifically,

By symmetry, each radius bisects one of these angles. Specifically,

By the Same-Side Interior Angles Theorem, consecutive angles of a parallelogram are supplementary - that is, their measures total . However,

,

violating these conditions. Therefore, Quadrilateral is not a parallelogram.

A rectangle is a parallelogram with four right angles.

Consecutive angles of a parallelogram are supplementary. If one angle of a parallelogram is given to be right, then its neighboring angles, being supplementary to a right angle, are right as well; also, opposite angles of a parallelogram are congruent, so the opposite angle is also right. All four angles must be right, making the parallelogram a rectangle by definition.

, making and supplementary. By the Converse of the Same Side Interior Angles Theorem, , it does follow that . However, without knowing the measures of the other two angles, nothing further can be concluded about Quadrilateral . Below are a parallelogram and a trapezoid, both of which have these two angles of these measures.

By the Same-Side Interior Angles Theorem, consecutive angles of a parallelogram can be proved to be supplementary - that is, their angle measures total . Specifically, and are a pair of supplementary angles. Since they are also congruent, it follows that both are right angles. For the same reason, and are also right angles. The parallelogram, having four right angles, is a rectangle by definition.

Opposite angles are equal, and adjacent angles must sum to 180.

Therefore, we can set up an equation to solve for z:

(z – 15) + 2z = 180

3z - 15 = 180

3z = 195

z = 65

Now solve for x:

2_z_ = x = 130°