SME
Grade 10 Math · Problem type
Angle expressions
Use this for “ℓ ∥ m, corresponding angles are (4x + 12)° and (2x + 50)°. Find x and the angle.”
Diagram
Corresponding angles 1 and 5: ∠1 = 88°, ∠5 = 88°, equal.
The lines are parallel (arrows): angles 1, 4, 5 and 8 are 88°; 2, 3, 6 and 7 are 92°.
t = 88°
t = 88°
This is an example. Type your own values to start a new problem.
(
p
x
+
q
)°
=
(
r
x
+
s
)°
x
x
worked out (not typed)
t
The angle
worked out (not typed) · °
Formulas
p
×
x
+
q
=
r
×
x
+
s
4 × 19 + 12 = 2 × 19 + 50
t
=
p
×
x
+
q
88 = 4 × 19 + 12
Assumptions
•
The lines are parallel, so the two corresponding angles are congruent: set the expressions equal.
•
Solve for x, then put it back to find the angle.
•
An angle here must be between 0° and 180°.
Step-by-step
WE KNOW
p = 4, q = 12, r = 2, s = 50
FIND
x (x), the angle (t)
Step 1 · Find x (x)
Use p × x + q = r × x + s
Take
the
smaller
x
term
from
both
sides,
then
the
number
beside
the
x
left,
then
divide.
x
=
s
−
q
p
−
r
x
=
50 − 12
4 − 2
Take
2
x
from
both
sides:
2
x
+
12
=
50
Take
12
from
both
sides:
2
x
=
38
Divide
both
sides
by
2:
x
=
19
x
=
19
Step 2 · Find the angle (t)
Use t = p × x + q
Put
x
back
into
the
first
angle.
t
=
4
×
19
+
12
t
=
76
+
12
t
=
88°
Check
Put the numbers back in. Both sides should match.
4 × 19 + 12 = 2 × 19 + 50 ✓
88 = 4 × 19 + 12 ✓
Topic check
See what you know: 5 questions on this topic
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