Angles

10 Grade 7 Mathematics questions on Angles, with worked marking schemes. 10 questions are available on this topic in full.

1. Question 1

   1 mark

   Two parallel lines are cut by a transversal. If one angle is 65°, the co-interior angle is:

   A. 65°

   B. 125°

   C. 115°

   D. 55°

   (1 mark)

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2. Question 2

   1 mark

   An exterior angle of a regular polygon is 40°. How many sides?

   A. 36

   B. 10

   C. 9

   D. 8

   (1 mark)

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3. Question 3

   1 mark

   Angles on a straight line are x, 2x, and 3x. Find x.

   A. 90°

   B. 60°

   C. 45°

   D. 30°

   (1 mark)

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4. Question 4

   4 marks

   A triangle has angles (2x+10)°, (3x)°, and (x+50)°. Find x and all angles.

   (4 marks)

   Marking scheme

   The angles of a triangle add up to $180^{\circ }$, so $(2x+10)+3x+(x+50)=180$. (1)

   Collect the terms: $6x+60=180$. (1)

   Solve: $6x=120$, so $x=20$. (1)

   Substitute back: $2(20)+10=50^{\circ }$, $3(20)=60^{\circ }$, $20+50=70^{\circ }$. (1)

   Final answer: $x=20$, and the angles are $50^{\circ }$, $60^{\circ }$ and $70^{\circ }$. Check: $50+60+70=180$.

5. Question 5

   1 mark

   Each interior angle of a regular hexagon is:

   A. 90°

   B. 60°

   C. 108°

   D. 120°

   (1 mark)

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6. Question 6

   2 marks

   Find the sum of interior angles of an octagon.

   (2 marks)

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7. Question 7

   1 mark

   The sum of interior angles of a pentagon is:

   A. 720°

   B. 360°

   C. 180°

   D. 540°

   (1 mark)

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8. Question 8

   2 marks

   Find the interior angle of a regular 12-sided polygon.

   (2 marks)

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9. Question 9

   3 marks

   Two angles of a quadrilateral are 85° and 110°. The other two are equal. Find them.

   (3 marks)

   Marking scheme

   The angles of a quadrilateral add up to $360^{\circ }$. Let each of the equal angles be $x$. (1)

   Then $85^{\circ }+110^{\circ }+x+x=360^{\circ }$, so $195^{\circ }+2x=360^{\circ }$ and $2x=165^{\circ }$. (1)

   Divide by $2$: $x=82.5^{\circ }$. (1)

   Final answer: each of the other two angles is $82.5^{\circ }$.

10. Question 10

    1 mark

    The sum of exterior angles of any polygon is:

    A. 180°

    B. 360°

    C. 540°

    D. 720°

    (1 mark)

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