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8th grade Angles of a triangle: the sum and the exterior angle worksheet

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Angles of a triangle: the sum and the exterior angle

Grade 8 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

  1. Luz measures two angles of a triangular sail: 46° and 57°. How many degrees is the third angle?

  2. Milo measures two angles of a triangular ramp side: 38° and 69°. How many degrees is the third angle?

  3. Noah measures two angles of a triangular tent end: 26° and 84°. How many degrees is the third angle?

  4. Bo builds an isosceles sail frame. The top angle is 100°. How many degrees is each base angle?

  5. Esme builds an isosceles roof frame. Each base angle is 65°. How many degrees is the top angle?

  6. Ren draws triangle GHQ and extends side GH past corner H. The outside angle at H is 118° and angle G is 47°. How many degrees is angle Q?

  7. Ari draws triangle DFG and extends side DF past corner F. The outside angle at F is 141° and angle D is 63°. How many degrees is angle G?

  8. Bo draws triangle CDF and extends side CD past corner D. Angle C is 50° and angle F is 60°. Which equation finds x, the outside angle at D?

    • x = 180 − 50 − 60
    • x = 50 + 60
    • x = 60 − 50
  9. Jun draws triangle UVW and extends side UV past corner V. Angle U is 38° and angle W is 51°. Which equation finds x, the outside angle at V?

    • x = 38 + 51
    • x = 51 − 38
    • x = 180 − 38 − 51
  10. Kira draws triangle GHQ and extends side GH past corner H. Angle G is 64° and angle Q is 41°. Which equation finds x, the outside angle at H?

    • x = 64 − 41
    • x = 64 + 41
    • x = 180 − 64 − 41
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8th grade Angles of a triangle: the sum and the exterior angle worksheet – printable
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About this worksheet

Angles of a triangle: the sum and the outside angle. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find a triangle's third angle (180° in all), including in a right triangle (90° corner) and an isosceles triangle (two equal base angles).
  • I can find an outside angle two ways: 180° minus the inside angle next to it, or the two far angles added.
  • I can solve for x when angles are written with x, and give the angle the question asks for.
  • I can explain why the angles of a triangle add to 180°.

Standard: 8.G.A.5 (triangle sum, exterior angle)

Words to know

inside angle: An angle inside the triangle, at one of its three corners.

outside (exterior) angle: The angle outside the triangle at a corner, made when one side is extended.

far angles: The two inside angles that are not at the corner of the outside angle.

straight line: A line with no bend. Angles side by side along it add to 180°.

isosceles triangle: A triangle with two equal sides. Its two base angles are equal.

right triangle: A triangle with a 90° corner. Its other two angles add to 90°.

unknown angle: An angle we don't know yet, often written with x, like (3x + 30)°.

Common mistakes

Used 360° where the total is 180°: for the angles of a triangle, or for a straight line (360° is a full turn). Tear the corners off a paper triangle and line them up along a straight edge.

Used 90° (a square corner) where the angles make a straight line (180°).

Added the known angles where the missing angle is what is left of the total (or, for a far angle, what is left of the outside angle).

What to say

Ask: is this a straight line or a square corner?

Ask: is the missing angle the two angles together, or what is left?

Questions parents ask

What is the most common mistake with angles of a triangle: the sum and the exterior angle?

Used 360° where the total is 180°: for the angles of a triangle, or for a straight line (360° is a full turn). Tear the corners off a paper triangle and line them up along a straight edge.

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 8 math

See all grade 8 math

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