7 1 Interior And Exterior Angles Worksheet Answer Key - Fill and ... - Free Printable

Let’s solve each problem step by step.

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Problem 1: Find m∠B in quadrilateral ABCD

We are given angles at A (70°), C (35°), and D (90°).
The sum of interior angles in any quadrilateral is always 360°.

So:

m∠A + m∠B + m∠C + m∠D = 360°
70° + m∠B + 35° + 90° = 360°
Add known angles: 70 + 35 + 90 = 195°
Then: m∠B = 360° - 195° = 165°

✔ Answer for #1: 165

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Problem 2: Find m∠F in triangle DEF

Given: angle at E is 20°, angle at D is 90° (right angle symbol)
Sum of angles in a triangle is always 180°

So:

m∠D + m∠E + m∠F = 180°
90° + 20° + m∠F = 180°
110° + m∠F = 180°
m∠F = 180° - 110° = 70°

✔ Answer for #2: 70

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Problem 3: Find m∠G in triangle GHI

Angles given: H = 45°, I = 45°
Again, triangle → sum = 180°

m∠G + 45° + 45° = 180°
m∠G + 90° = 180°
m∠G = 90°

✔ Answer for #3: 90

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Problem 4: Find m∠L in triangle JKL

Angle at K is marked as 60°.
Angle at J is outside the triangle — it’s labeled 130°, but that’s an exterior angle.

Important rule: The measure of an exterior angle equals the sum of the two remote interior angles.

So, exterior angle at J (130°) = m∠K + m∠L
130° = 60° + m∠L
m∠L = 130° - 60° = 70°

✔ Answer for #4: 70

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Problem 5: Find m∠P in triangles NOP and QRS

Wait — this looks like two separate triangles? But the question says “m∠P = ___” and shows both triangles with some angles.

Looking closely: Triangle NOP has angles N=30°, O=50°, so we can find P.

In triangle NOP:
m∠N + m∠O + m∠P = 180°
30° + 50° + m∠P = 180°
80° + m∠P = 180°
m∠P = 100°

Triangle QRS seems to be extra info or maybe a distractor? Since the question asks only for m∠P, and P is in triangle NOP, we use that.

✔ Answer for #5: 100

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Problem 6: Find m∠WXY in triangle WXY

Points: W, X, Y. Angle at Y is 30°, angle at W is 40°.
But wait — point X is on a straight line with another point? There’s a horizontal line through X, and angle between WX and the line is not given directly.

Actually, looking again: It says “m∠WXY”, which is the angle at vertex X in triangle WXY.

We’re told angle at W is 40°, angle at Y is 30°. So in triangle WXY:

m∠W + m∠X + m∠Y = 180°
40° + m∠WXY + 30° = 180°
70° + m∠WXY = 180°
m∠WXY = 110°

Wait — but there’s also a label “X” on a straight line with another segment going down to Y. Is that affecting anything?

Actually, no — because ∠WXY is clearly the angle inside triangle WXY at point X. The other lines might be there to confuse, but unless specified otherwise, we go by the triangle.

Alternatively, if the diagram shows that angle at X is formed with a straight line, then perhaps we need to consider supplementary angles? Let me recheck.

Looking at the description: “m∠WXY” — that’s the angle at X between points W, X, Y. In the diagram, if X is on a straight line and Y is below, then maybe the 30° is adjacent?

Wait — actually, let’s think differently. If angle at Y is 30°, and angle at W is 40°, then yes, angle at X must be 110° to make 180°.

But here’s a catch: sometimes diagrams show exterior angles. However, since no indication of that, and the question just says “find m∠WXY”, and gives two other angles in the same triangle, we proceed with 180° total.

✔ Answer for #6: 110

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Now questions 7–12 are fill-in-the-blank conceptual questions.

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Question 7: The sum of the angle measures of a quadrilateral is ___.

As used earlier: 360 degrees

✔ Answer: 360°

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Question 8: The acute angles of a _________ triangle are complementary.

Complementary means they add up to 90°. That happens in a right triangle, because one angle is 90°, so the other two must add to 90°.

✔ Answer: right

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Question 9: The measure of an _________ angle of a triangle is equal to the sum of the measures of its remote interior angles.

This is the definition of an exterior angle.

✔ Answer: exterior

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Question 10: The angle measures of a triangle are x, 3x, and 5x. Tell the measure of each angle.

Sum = x + 3x + 5x = 9x
Set equal to 180°:
9x = 180°
x = 20°

So angles are:
x = 20°
3x = 60°
5x = 100°

✔ Answers: 20°, 60°, 100°

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Question 11: You know that one of the exterior angles of an isosceles triangle is 140°. The angle measures of the triangle could be ___, ___, ___ or ___, ___, ___.

Exterior angle = 140° → so the adjacent interior angle = 180° - 140° = 40°

Since it’s an isosceles triangle, two angles are equal.

Case 1: The 40° angle is the vertex angle (the unique one). Then the base angles are equal.

Sum of base angles = 180° - 40° = 140° → each base angle = 70°

So angles: 40°, 70°, 70°

Case 2: The 40° angle is one of the base angles. Then the other base angle is also 40°, and the vertex angle = 180° - 40° - 40° = 100°

So angles: 40°, 40°, 100°

Both are valid isosceles triangles.

✔ Answers: 40°, 70°, 70° or 40°, 40°, 100°

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Final Answers compiled:

1. 165
2. 70
3. 90
4. 70
5. 100
6. 110
7. 360°
8. right
9. exterior
10. 20°, 60°, 100°
11. 40°, 70°, 70° or 40°, 40°, 100°

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Final Answer:
1. 165
2. 70
3. 90
4. 70
5. 100
6. 110
7. 360°
8. right
9. exterior
10. 20°, 60°, 100°
11. 40°, 70°, 70° or 40°, 40°, 100°