Geometry · Angles · 1.4

Vertical angles.

When two lines cross, the angles directly across from each other (vertical angles) are equal, and angles side by side are supplementary (add to 180°). So one angle fixes all four.

01 / THE IDEA

See it work.

Watch the method

Vertical angles

Vertical angles are equal; neighbors are supplementary.

1 / 2
1

Area of a rectangle

Area is length times width.

l×wl \times w
2

Multiply

Multiply the two dimensions.

70×undefined=NaN70 \times undefined = NaN
— / WHY IT WORKS

The idea underneath.

An X of angles

Two crossing lines make two pairs of equal vertical angles.

Why it works

Opposite angles match.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Two lines cross. One of the angles is 32°. What is the angle directly across from it (its vertical angle)?

1

Answer

32°

EX 2medium

Two lines cross. One of the angles is 39°. What is the angle directly across from it (its vertical angle)?

1

Answer

39°

EX 3hard

Two lines cross. One of the angles is 53°. What is the angle directly across from it (its vertical angle)?

1

Answer

53°

04 / COMMON TRAPS

Where students slip.

Trap

Thinking vertical angles are supplementary.

Fix

Across-the-X angles are EQUAL.

Trap

Mixing up neighbors and opposites.

Fix

Neighbors add to 180°; opposites are equal.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Two lines cross. One of the angles is 111°. What is the angle directly across from it (its vertical angle)?

Need a hint?
  • Angles across the crossing are equal.
  • Neighboring angles add to 180°.
C2

Two lines cross. One of the angles is 44°. What is the angle directly across from it (its vertical angle)?

Need a hint?
  • Angles across the crossing are equal.
  • Neighboring angles add to 180°.
C3

Two lines cross. One of the angles is 47°. What is the angle directly across from it (its vertical angle)?

Need a hint?
  • Angles across the crossing are equal.
  • Neighboring angles add to 180°.
C4

Two lines cross. One of the angles is 35°. What is the angle directly across from it (its vertical angle)?

Need a hint?
  • Angles across the crossing are equal.
  • Neighboring angles add to 180°.
Apply

Apply (4)

A1

Two lines cross. One of the angles is 48°. What is the angle directly across from it (its vertical angle)?

Need a hint?
  • Angles across the crossing are equal.
  • Neighboring angles add to 180°.
A2

Two lines cross. One of the angles is 138°. What is the angle directly across from it (its vertical angle)?

Need a hint?
  • Angles across the crossing are equal.
  • Neighboring angles add to 180°.
A3

Two lines cross. One of the angles is 143°. What is the angle directly across from it (its vertical angle)?

Need a hint?
  • Angles across the crossing are equal.
  • Neighboring angles add to 180°.
A4

Two lines cross. One of the angles is 74°. What is the angle directly across from it (its vertical angle)?

Need a hint?
  • Angles across the crossing are equal.
  • Neighboring angles add to 180°.
Extension

Extension (4)

E1

Two lines cross. One of the angles is 69°. What is the angle directly across from it (its vertical angle)?

Need a hint?
  • Angles across the crossing are equal.
  • Neighboring angles add to 180°.
E2

Two lines cross. One of the angles is 66°. What is the angle directly across from it (its vertical angle)?

Need a hint?
  • Angles across the crossing are equal.
  • Neighboring angles add to 180°.
E3

Two lines cross. One of the angles is 94°. What is the angle directly across from it (its vertical angle)?

Need a hint?
  • Angles across the crossing are equal.
  • Neighboring angles add to 180°.
E4

Two lines cross. One of the angles is 99°. What is the angle directly across from it (its vertical angle)?

Need a hint?
  • Angles across the crossing are equal.
  • Neighboring angles add to 180°.