SME
Grade 7 Math · Problem type
Unknown angles with an equation
Use this for “Two supplementary angles: one is twice the other. Find both.”
Diagram
a + b = 180°
60° + 120° = 180°
Supplementary angles: together they make a straight line.
This is an example. Type your own values to start a new problem.
a
°
+
k
×
a
°
=
180°
(1
+
k
)
×
a
°
=
180°
b
Bigger angle
worked out (not typed) · °
Formulas
a
=
180
÷
(1
+
k
)
(smaller
angle
=
180
÷
(1
+
times
as
big))
60 = 180 ÷ (1 + 2)
b
=
k
×
a
(bigger
angle
=
times
as
big
×
smaller
angle)
120 = 2 × 60
Assumptions
•
Call the smaller angle a. The bigger one is k times as big: k × a.
•
Together they make a straight line: a + k × a = 180, so (1 + k) × a = 180.
•
Divide 180 by 1 + k for the smaller angle.
•
With k = 1 the two angles are equal.
Step-by-step
WE KNOW
k = 2 (times as big)
FIND
smaller angle (a), bigger angle (b)
Step 1 · Find smaller angle (a)
Use a = 180 ÷ (1 + k) (smaller angle = 180 ÷ (1 + times as big))
a
and
k
×
a
make
180,
so
1
+
k
of
the
smaller
angle
make
180.
a
=
180
1 + 2
a
=
180
3
a
=
60°
Step 2 · Find bigger angle (b)
Use b = k × a (bigger angle = times as big × smaller angle)
The
bigger
angle
is
k
times
the
smaller.
b
=
2
×
60
b
=
120°
Check
Put the numbers back in. Both sides should match.
60 = 180 ÷ (1 + 2) ✓
120 = 2 × 60 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Related lessons
Supplementary, complementary, vertical and adjacent angles
Main lesson
Complementary angles
Use this for “Two angles make a right angle. One is 35°. What is the other?”
Vertical angles
Use this for “Two lines cross. One angle is 50°. Find the other three.”
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.”
Parallel lines and a transversal
Use this for “Lines ℓ and m are parallel. Angle 1 is 50°. Which angles are 50° and which are 130°?”
Which kind of angle pair?
Use this for “Are these angles complementary, supplementary or vertical?”
Can the sides make a triangle?
Use this for “Can sticks of 2, 3 and 6 inches make a triangle?”