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Geometry: Equations, Angles and Area
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Geometry: Equations, Angles and Area
Evie and Mason are preparing a course map for the sailing club. Solve each geometry puzzle, show the equation you use, and include units where needed. Angle diagrams are not drawn to scale.
Angle clues
Use angle facts to decode the turns and intersections on the club's route.
1.At a marker, two angles on a straight course line are (4x + 12)° and (2x + 24)°. Write an equation, solve for x, and give both angle sizes.
2.Two parallel ropes are crossed by a flagpole. One corresponding angle is 63°. What is the size of the matching corresponding angle? State the angle rule.
3.At a crossing, vertically opposite angles are (5x − 8)° and (3x + 28)°. Find x and the size of each of these angles.
4.The three angles in a triangular sail are 48°, 67° and x°. Calculate x and name the fact that makes your equation work.
Shapes for the shoreline
Now help the crew estimate spaces and lengths on its temporary base.
5.A quadrilateral-shaped deck panel has angles 86°, 104°, 95° and x°. Find x. Use the fact about the angle total in a quadrilateral.
6.A regular octagonal signal platform has eight equal interior angles. Work out the size of one interior angle.
7.A rectangular equipment mat measures 7.5 m by 4 m. Calculate its area and perimeter.
8.Kirra is marking a triangular safety zone with a base of 9 m and a perpendicular height of 6 m. What is its area?
9.A parallelogram-shaped shade has a 8.4 m base and a perpendicular height of 3 m. Find the covered area.
10.A 5 km track is enlarged by a scale factor of 1.4. How long is the track in the enlarged version?
2 printable pages
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