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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 - Challenge Me

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

  1. Luz's sail is a triangle with angles x°, (2x)° and (3x + 30)°. How many degrees is the largest angle?

  2. Noah's tent is a triangle with angles x°, (4x − 25)° and (5x + 35)°. How many degrees is the largest angle?

  3. Pia's kite wing is a triangle with angles x°, (4x + 20)° and (5x)°. How many degrees is the largest angle?

  4. Ren draws triangle DFG and extends side DF past corner F. Some of the angles use x. How many degrees is the outside angle at F?

  5. Tala draws triangle HQS and extends side HQ past corner Q. Some of the angles use x. How many degrees is the outside angle at Q?

  6. Bo's roof frame is an isosceles triangle with a top angle of 36°. The bottom beam sticks out past one bottom corner. How many degrees is the outside angle at that corner?

  7. Luz extends two sides of triangle CDF. The outside angle at C is 128° and at D is 111°. How many degrees is the inside angle at F?

  8. Tala draws triangle CDF on paper and extends side CD past D. Why is the outside angle at D equal to angle C plus angle F?

    • The outside angle is the biggest angle in the picture, so it is the sum of the others
    • The outside angle and the inside angle at D make 180°, and the three inside angles also make 180°
    • The outside angle and the inside angle at D make 360°, and the three inside angles make 180°

  9. Zee cuts three copies of a right triangle and lines them up along a ruler. Why do the three angles of the right triangle add to 180°?

    • The triangle has a 90° corner, and the other two corners are 45° each, so 90 + 45 + 45 = 180
    • Three copies fit corner to corner around a point, and a full turn is 360°
    • Three copies fit corner to corner along a straight line, and a straight line is 180°

  10. Luz extends one side at each corner of triangle CDF, going around the same way. The outside angles are 128°, 111° and 121°. What do the three outside angles add to?

    • 540°: three straight lines
    • 360°: a full turn
    • 180°: a straight line
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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

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