SME
Grade 7 Math · Problem type
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°?”
Diagram
Angles 1, 3, 5 and 7: a = 50°
Angles 2, 4, 6 and 8: b = 130°
a + b = 180°
Corresponding angles (1 and 5), alternate interior angles (3 and 5) and vertical angles (1 and 3) are equal.
This is an example. Type your own values to start a new problem.
a
°
+
b
°
=
180°
Formulas
a
+
b
=
180
(angle
1
+
angle
2
=
180)
50 + 130 = 180
Assumptions
•
When parallel lines are cut by a third line, the eight angles have only two sizes.
•
Corresponding, alternate interior and vertical angles are equal.
•
Any two angles side by side on a line add to 180°.
Step-by-step
WE KNOW
a = 50° (angle 1)
FIND
angle 2 (b)
Step 1 · Find angle 2 (b)
Use a + b = 180 (angle 1 + angle 2 = 180)
The two angles make a straight line. Take the other angle away from 180°.
50
+
b
=
180
b
=
180
−
50
b
=
130°
Check
Put the numbers back in. Both sides should match.
50 + 130 = 180 ✓
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.”
Unknown angles with an equation
Use this for “Two supplementary angles: one is twice the other. Find both.”
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.”
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?”