SME
Grade 10 Math · Problem type
Angles of a parallelogram
Use this for “In parallelogram ABCD, m∠A = 58°. Find m∠B and m∠C.”
Diagram
A parallelogram: opposite sides parallel and equal, opposite angles equal; the diagonals cut each other in half.
m∠A = 58°
m∠B = 122°
m∠C = 58°
This is an example. Type your own values to start a new problem.
m∠A
°
+
m∠B
°
=
180°
m∠C
m∠C
calculated · °
Formulas
m∠B = 180 − m∠A
122 = 180 − 58
m∠C = m∠A
58 = 58
Assumptions
•
Opposite sides are parallel and equal, and the diagonals cut each other in half.
•
Angles next to each other add to 180°, because the sides are parallel.
•
Opposite angles are equal: m∠C = m∠A and m∠D = m∠B.
Step-by-step
WE KNOW
m∠A = 58°
FIND
m∠B (m∠B), m∠C (m∠C)
Step 1 · Find m∠B (m∠B)
Use m∠B = 180 − m∠A
Angles next to each other in a parallelogram add to 180°.
m∠B = 180 − 58
m∠B = 122°
Step 2 · Find m∠C (m∠C)
Use m∠C = m∠A
Opposite angles of a parallelogram are equal.
m∠C = 58°
Check
Put the numbers back in. Both sides should match.
122 = 180 − 58 ✓
58 = 58 ✓
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Quadrilaterals and other polygons: angle sums and properties
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Rectangle and its diagonals
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