7th Grade Math · Unit 8
Quadrilateral angles sum to 360°. In a parallelogram, opposite angles are equal and consecutive angles are supplementary.
Quadrilateral sum
The interior angles of a quadrilateral sum to 360°.
Opposite angles
Opposite angles of a parallelogram are equal.
Consecutive angles
Consecutive angles of a parallelogram are supplementary.
Supplementary angles sum to 180°.
Rectangle and isosceles trapezoid
Every angle of a rectangle is 90°.
On an isosceles trapezoid, the two angles on the same base are equal. A consecutive angle along a leg is supplementary to that base angle.
Three angles are known. Find the fourth.
The interior angles of a quadrilateral sum to 360°.
85° + 95° + 100° + unknown = 360°
unknown = 360° − 280°
unknown = 80°
Answer: 80°
The interior angles of a quadrilateral sum to 360°.
75° + 85° + 90° + unknown = 360°
unknown = 360° − 250°
unknown = 110°
Answer: 110°
The interior angles of a quadrilateral sum to 360°.
55° + 65° + 70° + unknown = 360°
unknown = 360° − 190°
unknown = 170°
Answer: 170°
The interior angles of a quadrilateral sum to 360°.
100° + 90° + 60° + unknown = 360°
unknown = 360° − 250°
unknown = 110°
Answer: 110°
The interior angles of a quadrilateral sum to 360°.
45° + 55° + 65° + unknown = 360°
unknown = 360° − 165°
unknown = 195°
Answer: 195°
The interior angles of a quadrilateral sum to 360°.
90° + 80° + 70° + unknown = 360°
unknown = 360° − 240°
unknown = 120°
Answer: 120°
The interior angles of a quadrilateral sum to 360°.
115° + 75° + 50° + unknown = 360°
unknown = 360° − 240°
unknown = 120°
Answer: 120°
The interior angles of a quadrilateral sum to 360°.
100° + 100° + 80° + unknown = 360°
unknown = 360° − 280°
unknown = 80°
Answer: 80°
The interior angles of a quadrilateral sum to 360°.
35° + 45° + 55° + unknown = 360°
unknown = 360° − 135°
unknown = 225°
Answer: 225°
The interior angles of a quadrilateral sum to 360°.
130° + 70° + 40° + unknown = 360°
unknown = 360° − 240°
unknown = 120°
Answer: 120°
The interior angles of a quadrilateral sum to 360°.
72° + 84° + 96° + unknown = 360°
unknown = 360° − 252°
unknown = 108°
Answer: 108°
Opposite angles match. Consecutive angles sum to 180°.
Opposite angles of a parallelogram are equal.
The opposite angle is 70°.
Answer: 70°
Opposite angles of a parallelogram are equal.
The opposite angle is 50°.
Answer: 50°
Opposite angles of a parallelogram are equal.
The opposite angle is 60°.
Answer: 60°
Opposite angles of a parallelogram are equal.
The opposite angle is 80°.
Answer: 80°
Opposite angles of a parallelogram are equal.
The opposite angle is 110°.
Answer: 110°
Opposite angles of a parallelogram are equal.
The opposite angle is 120°.
Answer: 120°
Consecutive angles of a parallelogram are supplementary.
unknown + 40° = 180°
unknown = 140°
Answer: 140°
Consecutive angles of a parallelogram are supplementary.
unknown + 55° = 180°
unknown = 125°
Answer: 125°
Consecutive angles of a parallelogram are supplementary.
unknown + 65° = 180°
unknown = 115°
Answer: 115°
Consecutive angles of a parallelogram are supplementary.
unknown + 75° = 180°
unknown = 105°
Answer: 105°
Consecutive angles of a parallelogram are supplementary.
unknown + 85° = 180°
unknown = 95°
Answer: 95°
Rectangles are all right angles. Isosceles trapezoid base angles match.
Every angle of a rectangle is a right angle.
Each angle measures 90°.
The other three angles are 90°, 90°, and 90°.
Answer: 90°, 90°, and 90°
Every angle of a rectangle is a right angle.
Each angle measures 90°.
The other three angles are 90°, 90°, and 90°.
Answer: 90°, 90°, and 90°
Every angle of a rectangle is a right angle.
Each angle measures 90°.
The other three angles are 90°, 90°, and 90°.
Answer: 90°, 90°, and 90°
The two angles on the same base of an isosceles trapezoid are equal.
The other angle on that base is 70°.
Consecutive angles between the parallel sides are supplementary.
180° − 70° = 110°
That consecutive angle is 110°.
Answer: 70° on that base, and 110° along a leg
The two angles on the same base of an isosceles trapezoid are equal.
The other angle on that base is 60°.
Consecutive angles between the parallel sides are supplementary.
180° − 60° = 120°
That consecutive angle is 120°.
Answer: 60° on that base, and 120° along a leg
The two angles on the same base of an isosceles trapezoid are equal.
The other angle on that base is 65°.
Consecutive angles between the parallel sides are supplementary.
180° − 65° = 115°
That consecutive angle is 115°.
Answer: 65° on that base, and 115° along a leg
The two angles on the same base of an isosceles trapezoid are equal.
The other angle on that base is 80°.
Consecutive angles between the parallel sides are supplementary.
180° − 80° = 100°
That consecutive angle is 100°.
Answer: 80° on that base, and 100° along a leg
The two angles on the same base of an isosceles trapezoid are equal.
The other angle on that base is 50°.
Consecutive angles between the parallel sides are supplementary.
180° − 50° = 130°
That consecutive angle is 130°.
Answer: 50° on that base, and 130° along a leg
The two angles on the same base of an isosceles trapezoid are equal.
The other angle on that base is 75°.
Consecutive angles between the parallel sides are supplementary.
180° − 75° = 105°
That consecutive angle is 105°.
Answer: 75° on that base, and 105° along a leg
The two angles on the same base of an isosceles trapezoid are equal.
The other angle on that base is 55°.
Consecutive angles between the parallel sides are supplementary.
180° − 55° = 125°
That consecutive angle is 125°.
Answer: 55° on that base, and 125° along a leg
The two angles on the same base of an isosceles trapezoid are equal.
The other angle on that base is 40°.
Consecutive angles between the parallel sides are supplementary.
180° − 40° = 140°
That consecutive angle is 140°.
Answer: 40° on that base, and 140° along a leg
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