Geometry · Ordinary Level
Angles in a Triangle
Ordinary Level · Class 3 · Tap NEXT to begin
Section 1 of 2
The Angles Add to 180°
Triangle rule
The three angles inside any triangle add up to $180^\circ$.
Worked example — find the third angle
Find $A$.
$A + 80 + 30 = 180$
$A + 110 = 180 \Rightarrow A = 70^\circ$
$A = 70^\circ$
Worked example — angles in terms of A
A triangle has angles $A$, $2A$ and $30^\circ$. Find $A$.
$A + 2A + 30 = 180$
$3A + 30 = 180 \Rightarrow 3A = 150$
$A = 50^\circ$
$A = 50^\circ$
Section 2 of 2
The Exterior Angle
Exterior = sum of the two far angles
An exterior angle of a triangle equals the sum of the two interior angles opposite it.
Worked example — exterior angle
A triangle has interior angles $A$ and $60^\circ$, and the exterior angle at the third vertex is $3A$. Find $A$.
$3A = A + 60$ (exterior $=$ sum of the two opposite interior angles)
$3A - A = 60 \Rightarrow 2A = 60$
$A = 30^\circ$
$A = 30^\circ$
You try
A triangle has interior angles $A$ and $60^\circ$, with exterior angle $4A$ at the third vertex. Find $A$.
$4A = A + 60$.
$4A = A + 60 \Rightarrow 3A = 60$
$A = 20^\circ$
$A = 20^\circ$
You try
Find $A$ and $B$: $3A$ sits on a straight line with $60^\circ$, and $4B$ sits on a straight line with $80^\circ$.
Straight line $= 180$.
$3A + 60 = 180 \Rightarrow 3A = 120 \Rightarrow A = 40^\circ$
$4B + 80 = 180 \Rightarrow 4B = 100 \Rightarrow B = 25^\circ$
$A = 40^\circ,\ B = 25^\circ$
That’s Class 3.
Angle sum ($180^\circ$) and the exterior-angle rule. Class 4: special triangles.