SME
Grade 10 Math · Problem type
Opposite angles of an inscribed quadrilateral
Use this for “ABCD is inscribed in a circle and m∠A = 84°. Find m∠C.”
Diagram
Opposite angles of an inscribed quadrilateral add to 180°: each is half the arc across from it, and those two arcs make the whole circle.
∠A stands on the blue arc BCD, ∠C on the yellow arc DAB.
m∠A + m∠C = 84° + 96° = 180°.
This is an example. Type your own values to start a new problem.
m∠A
°
+
m∠C
°
=
180°
Formulas
m∠A + m∠C = 180
84 + 96 = 180
Assumptions
•
ABCD is inscribed: all four corners are on the circle.
•
Each angle is half the arc across from it; the arcs across from A and from C make the whole circle.
•
So opposite angles add to 180°: m∠A + m∠C = 180° and m∠B + m∠D = 180°.
Step-by-step
WE KNOW
m∠A = 84°
FIND
m∠C (m∠C)
Step 1 · Find m∠C (m∠C)
Use m∠A + m∠C = 180
Opposite angles of an inscribed quadrilateral add to 180°.
m∠C = 180 − m∠A
m∠C = 180 − 84
m∠C = 96°
Check
Put the numbers back in. Both sides should match.
84 + 96 = 180 ✓
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