SME
Grade 7 Math · Problem type
Angles in a triangle
Use this for “A triangle has angles of 54° and 71°. What is the third?” or “An exterior angle is 125° and one far angle is 54°. Find the other far angle.”
Diagram
a + b + c = 180°
54° + 71° + 55° = 180°
The exterior angle e = a + b = 125°: it and c make a straight line.
This is an example. Type your own values to start a new problem.
a
°
+
b
°
+
c
°
=
180°
e
Exterior angle at c
calculated · °
Formulas
a
+
b
+
c
=
180
(first
angle
+
second
angle
+
third
angle
=
180)
54 + 71 + 55 = 180
e
+
c
=
180
(exterior
angle
at
c
+
third
angle
=
180)
125 + 55 = 180
Assumptions
•
The three angles of any triangle add to 180°.
•
An exterior angle and the angle beside it make a straight line.
•
So an exterior angle equals the sum of the two far angles.
Step-by-step
WE KNOW
a = 54° (first angle), b = 71° (second angle)
FIND
third angle (c), exterior angle at c (e)
Step 1 · Find third angle (c)
Use a + b + c = 180 (first angle + second angle + third angle = 180)
The three angles make 180°: take the other two away.
54
+
71
+
c
=
180
c
=
180
−
54
−
71
c
=
126
−
71
c
=
55°
Step 2 · Find exterior angle at c (e)
Use e + c = 180 (exterior angle at c + third angle = 180)
The
exterior
angle
and
c
make
a
straight
line.
It
equals
a
+
b
.
e
+
55
=
180
e
=
180
−
55
e
=
125°
Check
Put the numbers back in. Both sides should match.
54 + 71 + 55 = 180 ✓
125 + 55 = 180 ✓
Topic check
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