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Grade 7 · unit review

Review: Scale Drawings and Connected Angle Relationships

A scale drawing links represented and actual lengths through a fixed factor. Geometric relationships connect angles through straight lines and triangles, so a justified equation can replace guessing from a sketch.

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Bring the unit skills together

Use these 4 new cases to check your reasoning. Choices are temporary and are not saved to an account, sent to staff or recorded as school grades. Download your current review choices before leaving or reloading.

Unit review questions
1. An original plan uses 1 cm for 4 m. A corridor is 7 cm on the plan. What actual length does the plan represent?
Need a hint?
  • A scale ratio says how much actual length corresponds to each drawing unit.
  • The drawing is a model rather than proof of an actual measured corridor.
2. A scale drawing uses 1 cm for 3 m. A rectangular region is 7 cm by 8 cm on the drawing. What actual area is represented?
Need a hint?
  • Area is built from two lengths, so scaling both by the same factor multiplies area by the factor squared.
  • A length scale factor is not automatically the area factor.
3. Two adjacent angles form a straight angle. One is 55°. Find the other.
Need a hint?
  • Two adjacent angles whose outside rays form a straight line make a linear pair.
  • Adjacent angles need not be supplementary unless their outer rays form a straight line.
4. A triangle has two remote interior angles 40° and 55°. What is the exterior angle at its third vertex?
Need a hint?
  • A triangle’s interior angles total 180 degrees.
  • Use the two remote interior angles rather than including the adjacent third angle in their sum.

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Create a four-part mathematical solution sheet for these supplied cases. 1. An original plan uses 1 cm for 4 m. A corridor is 9 cm on the plan. What actual length does the plan represent? Candidate answers: (A) 35 m (B) 36 m (C) 37 m (D) 72 m. 2. A scale drawing uses 1 cm for 3 m. A rectangular region is 9 cm by 10 cm on the drawing. What actual area is represented? Candidate answers: (A) 270 m² (B) 57 m² (C) 810 m² (D) 90 m². 3. Two adjacent angles form a straight angle. One is 61°. Find the other. Candidate answers: (A) 119 ° (B) 180 ° (C) 29 ° (D) 61 °. 4. A triangle has two remote interior angles 42° and 57°. What is the exterior angle at its third vertex? Candidate answers: (A) 100 ° (B) 198 ° (C) 98 ° (D) 99 °.

Work on paper or in your own document. Explain the choices you made.

  • State each requested quantity or relationship and its input restrictions.
  • Show intermediate calculations or the applicable theorem with matching correspondences.
  • Give all four results, including exact values or requested rounding and units.
  • Check a result by substitution, reversal, dimensions, a representation or a counterexample as appropriate.
Compare with a model response

1. 36 m. Multiply 9 cm by 4 m/cm: 36 m. The centimeters cancel. This is a representation, not an on-site measurement. 2. 810 m². Actual sides are 27 m and 30 m. Area is their product, 810 m². A length scale of 3 makes an area scale of 9. 3. 119 °. A straight angle totals 180°. Subtract the known angle: 180−61=119°. Adjacency alone would not imply supplementary angles. 4. 99 °. The third interior angle is 180−42−57=81°. Its adjacent exterior angle is 180−(81)=99°, also the sum of the remote angles.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.