1. The sum of all interior angles of a quadrilateral is 360°.
2. Let the angles be x, 2x, 4x, and 5x.
x + 2x + 4x + 5x = 360°
12x = 360°
x = 30°
The angles are 30°, 60°, 120°, and 150°.
3. Let the two unknown angles be x and 2x.
90° + 90° + x + 2x = 360°
180° + 3x = 360°
3x = 180°
x = 60°
The angles are 90°, 90°, 60°, and 120°.
4. Let the complementary angles be a and b, so a + b = 90°.
Let the other two angles be 4y and 5y.
a + b + 4y + 5y = 360°
90° + 9y = 360°
9y = 270°
y = 30°
The two angles are 4y = 120° and 5y = 150°.
5. Let the fourth angle be x.
49° + 70° + 121° + x = 360°
240° + x = 360°
x = 120°
6. 7x + 5x + 3x + 3x = 360°
18x = 360°
x = 20°
7. Let the angles be 2x, 3x, 6x, and 7x.
2x + 3x + 6x + 7x = 360°
18x = 360°
x = 20°
The angles are 40°, 60°, 120°, and 140°.
8. In a parallelogram, opposite angles are equal and adjacent angles are supplementary.
If one angle is 90°, the opposite angle is also 90°.
The adjacent angles are 180° - 90° = 90°.
All four angles are 90°.
9. In parallelogram ABCD, opposite angles are equal.
∠A = ∠C = 50°
Adjacent angles are supplementary.
∠D = 180° - ∠A = 180° - 50° = 130°
10. In parallelogram PQRS, opposite angles are equal.
∠Q = ∠S = 95°
In triangle PQR, the sum of angles is 180°.
∠PQR = 95°, ∠PRQ = 35°, so ∠QPR = 180° - 95° - 35° = 50°.
Since PQRS is a parallelogram, ∠SPR = ∠QPR = 50° (alternate interior angles).
In triangle PSR, ∠PSR = 95°, ∠SPR = 50°, so ∠PRS = 180° - 95° - 50° = 35°.
But ∠PRS is part of ∠SRQ.
Actually, in parallelogram PQRS, ∠SRQ = ∠SPQ.
Consider triangle PQR: ∠PQR = 95°, ∠PRQ = 35°, so ∠QPR = 50°.
Since PQRS is a parallelogram, ∠SPQ = 180° - ∠PQR = 180° - 95° = 85°.
So ∠SPR = ∠SPQ - ∠QPR = 85° - 50° = 35°.
Now, in triangle PSR, ∠PSR = 95°, ∠SPR = 35°, so ∠PRS = 180° - 95° - 35° = 50°.
But we need ∠x which is ∠PRQ? No, the figure shows x at R, between PR and QR.
Re-examining: In triangle PQR, angles are ∠PQR=95°, ∠PRQ=x, ∠QPR=35°.
Sum is 180°, so 95° + x + 35° = 180°.
130° + x = 180°
x = 50°.
11. In parallelogram ABCD, adjacent angles are supplementary.
∠A + ∠B = 180°, but 120° + 60° = 180°, which is correct.
Opposite angles are equal.
∠D = ∠B = 60°
∠C = ∠A = 120°
Parent Tip: Review the logic above to help your child master the concept of quadrilateral worksheet answers.
