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Grade 7 Math · Problem type
Vertical angles
Use this for “Two lines cross. One angle is 50°. Find the other three.”
Diagram
a + b = 180°
50° + 130° = 180°
Vertical angles are equal: c = a = 50°.
This is an example. Type your own values to start a new problem.
a
°
+
b
°
=
180°
c
°
=
a
°
Formulas
a
+
b
=
180
(angle
a
+
angle
beside
it
=
180)
50 + 130 = 180
c
=
a
(angle
across
from
a
=
angle
a)
50 = 50
Assumptions
•
Two straight lines cross at one point and make four angles.
•
Angles next to each other on a line add to 180°.
•
Angles across from each other are vertical angles: they are equal.
Step-by-step
WE KNOW
a = 50° (angle a)
FIND
angle beside it (b), angle across from a (c)
Step 1 · Find angle beside it (b)
Use a + b = 180 (angle a + angle beside it = 180)
The two angles make a straight line. Take the other angle away from 180°.
50
+
b
=
180
b
=
180
−
50
b
=
130°
Step 2 · Find angle across from a (c)
Use c = a (angle across from a = angle a)
Vertical angles are across from each other, so they are equal.
c
=
50°
Check
Put the numbers back in. Both sides should match.
50 + 130 = 180 ✓
50 = 50 ✓
Topic check
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