SME
Grade 10 Math · Problem type
Triangle angle sum and exterior angle
Use this for “Side BC is extended to D. m∠A = 52° and m∠B = 71°. Find m∠ACD and m∠ACB.”
Diagram
This is an example. Type your own values to start a new problem.
m∠ACD
°
=
m∠A
°
+
m∠B
°
m∠ACB
m∠ACB
calculated · °
Formulas
m∠A + m∠B + m∠ACB = 180
52 + 71 + 57 = 180
m∠ACD = m∠A + m∠B
123 = 52 + 71
Assumptions
•
The three angles of a triangle add to 180°.
•
The exterior angle ∠ACD and ∠ACB make a straight line, so they add to 180°.
•
So the exterior angle equals the two remote interior angles added: m∠ACD = m∠A + m∠B.
Step-by-step
WE KNOW
m∠A = 52°, m∠B = 71°
FIND
m∠ACB (m∠ACB), m∠ACD (m∠ACD)
Step 1 · Find m∠ACB (m∠ACB)
Use m∠A + m∠B + m∠ACB = 180
The angles of a triangle add to 180°.
m∠ACB = 180 − m∠A − m∠B
m∠ACB = 180 − 52 − 71
m∠ACB = 57°
Step 2 · Find m∠ACD (m∠ACD)
Use m∠ACD = m∠A + m∠B
The exterior angle equals the two remote interior angles added (180° − m∠ACB).
m∠ACD = 52 + 71
m∠ACD = 123°
Check
Put the numbers back in. Both sides should match.
52 + 71 + 57 = 180 ✓
123 = 52 + 71 ✓
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Base angles of an isosceles triangle
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