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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

MEAP Preparation - Grade 7 Mathematics
4.14 Triangle Sum Theorem

"The sum of the measures of the angles of a triangle is 180°".
In ABC, mÐA + mÐb + mÐc = 1800

In the above triangle the sum of three angles is: 70 + 60 + 50 = 1800

Examples:

  1. In ABC, ÐA = 80° and ÐB = 70°, find ÐC = ?
    Solution:
    ÐA + ÐB = 80° + 70° = 150°. But Ð A + ÐB + ÐC = 180°.
    Therefore, ÐC = 180 ° - 150° = 30°.
  2. If the measures of the three angles of a triangle are x-2, x+6 and x+8, find them.

    The sum of the measures of the three angles x-2 + x+6 + x+8 = 3x+12.
    But the sum of the measures of the three angles of a triangle = 180°.
    Therefore, 3x+12 = 180°; 3x = 180 - 12 = 168.
    x = 168/3 = 56°.
    Therefore, x- 2 = 56-2 = 54°.
    Also x+6 = 56 + 6 = 62°.
    and x+8 = 56 + 8 = 64°.
    So, the measures of the angles are 54° 62° and 64°.
Directions: Answer the following questions.
1) Prove triangle sum theorem.
2) Prove the corollary to the triangle sum theorem: The acute angles of a right triangles are complementary.
3) Draw the triangles with the following measures, use a protractor to measure angles :
600-600-600 triangle,
500-700-600 triangle,
400- 500- 900 triangle
300- 600- 900 triangle
450- 450- 900 triangle
200- 500- 1800 triangle
1200- 200- 400 triangle
1400- 100- 300 triangle
1600- 100- 100 triangle
4) Draw 5 triangles and measure the interior angles using a protractor and prove that the sum of the measures is 180 degrees.

Q 1: In ABC, ÐA = 100°, ÐB = 50°, find ÐC.
35°
30°
60°
70°

 Q 2: In ABC, ÐA = 85°, ÐB = 45°, find ÐC.
70°
45°
50°
60°

Q 3: In ABCÐA = 60°, ÐB = 40°, find ÐC.
60°
45°
70°
80°

 Q 4: In ABC, ÐA = 70°, ÐB = 30°, find ÐC.
70°
60°
90°
80°

Q 5: If in ABC, ÐA = 90°, ÐB = 45°, then ÐC = ______.
60°
70°
50°
45°

 Q 6: In ABC, ÐA = 45°, ÐB = 90°, find ÐC.
45°
60°
45°
40°

Q 7: If 2x, x and 3x are the measures of the angles of a triangle, find the angles.
45°, 45° and 90°
90°, 45° and 30°
60°, 30° and 90°
90°, 30° and 60°

 Q 8: In ABC, ÐA = 100°, ÐB = 30°, find ÐC.
70°
50°
45°
60°

Question 9: This question is available to subscribers only!

 Question 10: This question is available to subscribers only!


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