SME
Grade 10 Math · Problem type
The angle in a semicircle
Use this for “AB is a diameter and m∠PAB = 34°. Find m∠PBA.”
Diagram
An angle inscribed in a semicircle is a right angle: it stands on a 180° arc.
a + b = 90°
34° + 56° = 90°
This is an example. Type your own values to start a new problem.
a
°
+
b
°
=
90°
Formulas
a
+
b
=
90
34 + 56 = 90
Assumptions
•
AB is a diameter, so its arc is 180° and the inscribed angle at P is half of it: 90°.
•
So the other two angles of △APB add to 90°.
•
Going the other way, an inscribed right angle always stands on a diameter.
Step-by-step
WE KNOW
a = 34°
FIND
m∠PBA (b)
Step 1 · Find m∠PBA (b)
Use a + b = 90
The angle at P is 90°, so the other two share 90°.
b
=
90
−
a
b
=
90
−
34
b
=
56°
Check
Put the numbers back in. Both sides should match.
34 + 56 = 90 ✓
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