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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 - 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 sketc... 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° (a) Work out the size of the third angle in the triangle BOP - 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 angles in a triangle is always 180°.
Let the third angle be denoted as angle A.
Thus, we have:
Simplifying this gives:
Subtracting 100° from both sides yields:
Therefore, the third angle is 80°.
Step 2
Draw a sketch of one such triangle BOP.
Answer
In sketching triangle BOP, we label it as follows:
- Side BO = 8 cm
- Angle B = 40°
- Angle O = 60°
- Angle P = 80°
The triangle should have a clear representation of all angles and the specified side lengths, ensuring accurate measurements for geometry.
Step 3
Construct the triangle BOP from your sketch.
Answer
To construct triangle BOP:
- Draw base BO = 8 cm.
- From point B, use a protractor to measure and draw angle B = 40°.
- From point O, measure and draw angle O = 60°.
- The intersection of the two lines will be point P.
- Connect points P and B, and points P and O to complete triangle BOP.