Vertically Opposite Angle Unknown Angle worksheet - Free Printable

Let’s solve each problem step by step.

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Problem 1:

We are given a diagram with intersecting lines and angles labeled:

- One angle is 70°
- Another angle next to it (on the same straight line) is made up of two parts: 33° and ∠e
- We need to find ∠e

Important idea: Angles on a straight line add up to 180°.

So, look at the bottom-left side — there’s a 70° angle. The angle directly opposite to it (vertically opposite) must also be 70°, because vertically opposite angles are equal.

Now, that 70° angle is part of a larger angle on the top-right side? Wait — let’s think again.

Actually, looking more carefully:

The 70° angle and the angle made of 33° + ∠e are vertically opposite? No — they’re not directly opposite.

Wait — better approach:

Look at the point where all lines meet. The angles around that point should add up to 360°, but we can use simpler ideas.

Notice: The 70° angle and the angle adjacent to it (which includes 33° and ∠e) form a straight line? Not exactly.

Actually, here’s the key:

The angle marked 70° and the angle composed of 33° + ∠e are vertically opposite angles — meaning they are across from each other at the intersection.

✔ Vertically opposite angles are EQUAL.

So:

> 33° + ∠e = 70°

Then:

> ∠e = 70° - 33° = 37°

✔️ That makes sense.

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Problem 2:

We have three angles meeting at a point:

- 81°
- 65°
- ∠d

And they appear to lie on a straight line? Or around a point?

Looking at the diagram description: It shows three angles around an intersection — likely forming a straight line or full circle.

But note: In the example at the top, they used the idea that angles on one side of a straight line add to 180°.

In this case, the 81°, 65°, and ∠d seem to be on the same side of a straight line — so together they make 180°.

Wait — actually, looking again: The red arcs suggest these are angles around a point, but possibly on a straight line.

Better clue: In many such problems, if three angles are shown meeting at a point along a straight line, their sum is 180°.

Assume that 81° + 65° + ∠d = 180° (because they lie on a straight line).

Then:

> 81 + 65 = 146

> ∠d = 180 - 146 = 34°

Alternatively, could they be around a full point? Then total would be 360° — but that doesn’t fit since only three angles are shown and no indication of others.

Also, in the first problem, we used vertical angles and straight lines — consistent with basic geometry for middle school.

Another way: Maybe 81° and 65° are on one side, and ∠d is vertically opposite to something? But the diagram isn't clear.

Wait — perhaps the 81° and 65° are adjacent, and ∠d is the remaining angle to complete the straight line.

Yes — that’s standard.

So:

Total on straight line = 180°

Given two angles: 81° and 65°

Sum = 81 + 65 = 146°

So ∠d = 180 - 146 = 34°

✔️ Confirmed.

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Final Answer:

∠e = 37°
∠d = 34°