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The triangle BOP has: one side that is 8 cm long one angle of 40° one angle of 60° - Junior Cycle Mathematics - Question 6 - 2016
Question 6
The triangle BOP has: one side that is 8 cm long one angle of 40° one angle of 60°. (a) Work out the size of the third angle in the triangle BOP. (b) Draw a sketch... show full transcript
Worked Solution & Example Answer:The triangle BOP has: one side that is 8 cm long one angle of 40° one angle of 60° - Junior Cycle Mathematics - Question 6 - 2016
Step 1
Work out the size of the third angle in the triangle BOP.
Answer
To find the third angle in triangle BOP, we use the property that the sum of the angles in a triangle is always 180°.
Let the third angle be represented as .
Thus, we can set up the equation:
Combining the known angles:
To isolate , we subtract 100° from both sides:
Therefore, the size of the third angle is 80°.
Step 2
Draw a sketch of one such triangle BOP.
Answer
- Begin by drawing a horizontal line representing side OP, 8 cm long.
- At point O, use a protractor to measure an angle of 40° and draw line OB.
- At point P, measure an angle of 60° and draw line PB.
- Let the intersection of those two lines be point B.
- Label the angles at each vertex:
- Angle O = 40°
- Angle P = 60°
- Angle B = 80°
Finally, ensure that all angles and the side length are clearly labeled for clarity.
Step 3
Construct the triangle BOP from your sketch.
Answer
- Using a ruler, draw a base line segment OP that is exactly 8 cm.
- At point O, accurately measure and construct an angle of 40° from the base OP, marking point B.
- At point P, accurately measure and construct an angle of 60° from the base OP, checking that it intersects with line OB at point B.
- Ensure all measurements are checked for accuracy.
- Label the triangle BOP, confirming that angle O = 40°, angle P = 60°, angle B = 80°, and side OP = 8 cm.