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Calculating Unknown Angles

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Calculating Unknown Angles

Use angle facts to find each unknown. Show your calculation where asked. Angles are measured in degrees (°).

Angle-finding at the skate park

The ramps and rails at a skate park create useful angle puzzles.

1.At a ramp, two adjacent angles lie on a straight line. One is 127°. What is the other angle?
2.Three angles meet at a point beside a rail. Two are 98° and 146°. Find the third angle.

Designing a triangular ramp

A triangular ramp has interior angles that add to 180°.

3.A triangular ramp has angles of 38° and 76°. Calculate the third angle.
4.A triangular sign has angles x°, 2x° and 3x°. Find x and then state all three angles.

Checking a four-sided design

The interior angles in any quadrilateral add to 360°.

5.A four-sided skate feature has three interior angles of 84°, 101° and 93°. Find its fourth angle.
6.A quadrilateral design has angles x°, (x + 20)°, 2x° and (x + 40)°. Find x and all four angles.

Angle clues in a parallel-rail puzzle

Two parallel rails are crossed by a straight support. Corresponding angles are equal, and adjacent angles on a straight line add to 180°.

7.Two parallel rails are crossed by a straight support. At the upper intersection, the angle above the upper rail and to the right of the support is 68°. The angle in the same position at the lower intersection is x°. Find x.
8.At the lower intersection of two parallel rails crossed by a straight support, x° is the angle above the lower rail and to the right of the support. Angle y° is adjacent to x° on the straight line formed by the lower rail. Find y.
9.A student says an angle next to 145° on a straight line must also be 145°. Is the student correct? Explain using an angle fact.
10.A designer writes two angles on a straight line as (3x + 10)° and (2x − 5)°. Find x and the size of each angle.

3 printable pages

  • Calculating Unknown Angles, page 1 of 3: Angle-finding at the skate park, Designing a triangular ramp

    Page 1

  • Calculating Unknown Angles, page 2 of 3: Checking a four-sided design, Angle clues in a parallel-rail puzzle

    Page 2

  • Calculating Unknown Angles, page 3 of 3: 10. A designer writes two angles on a straight line as

    Page 3

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