One angle of a parallelogram measures 113°. What are the measures of the other three angles in the parallelogram?
opposite angles of a parallelogram are congruent
so draw your diagram and it should be clear
In a parallelogram, opposite angles are congruent, which means they have the same measure. Since one angle of the parallelogram measures 113°, the opposite angle also measures 113°.
To find the measures of the other two angles, we know that the sum of the interior angles of any quadrilateral is 360°.
Let's denote the measure of one of the other two angles as "x".
Since the opposite angle is congruent, the other angle also measures "x" degrees.
Now, applying the property that the sum of the interior angles of a quadrilateral is 360°, we can set up the equation:
113° + 113° + x + x = 360°
Simplifying the equation:
226° + 2x = 360°
Subtracting 226° from both sides:
2x = 360° - 226°
2x = 134°
Dividing both sides by 2:
x = 134° / 2
x = 67°
Therefore, the measures of the other three angles in the parallelogram are 113°, 113°, and 67°.
To find the measures of the other three angles in a parallelogram, we need to use the property that opposite angles in a parallelogram are congruent. In other words, the opposite angles are equal in measure.
Since one angle of the parallelogram measures 113°, the opposite angle will also measure 113°. Therefore, we have two angles with measures of 113° each.
To find the measures of the other two angles, we can use the fact that the sum of the measures of the interior angles of a parallelogram is always 360°.
Let's denote the measures of the other two angles as x and y.
The sum of all four angles in a parallelogram is 360°:
113° + 113° + x + y = 360°
Now, we can solve for x and y.
Subtracting 226° from both sides of the equation:
x + y = 360° - 226°
x + y = 134°
Since the opposite angles in a parallelogram are congruent, the measures of the two remaining angles are equal. Let's assume that both x and y have the same measure, which we'll call z:
x = z
y = z
Substituting the values of x and y with z in the equation x + y = 134°:
z + z = 134°
2z = 134°
Dividing both sides of the equation by 2:
z = 67°
Therefore, the measures of the other two angles in the parallelogram are both 67°.