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Triangle Properties and Angles
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Triangle Properties and Angles
Solve each challenge. Show your working for calculations and give reasons where asked. Angles are in degrees.
Classify and calculate
Use triangle properties to identify and find missing angles.
1.A triangle has side lengths 7 cm, 7 cm and 10 cm. Classify it by its sides. What can you say about the angles opposite the two 7 cm sides?
2.Which description must be true of an obtuse triangle?
- It has one angle greater than 90°.
- It has two angles greater than 90°.
- All three angles are equal.
- It has one angle equal to 90°.
3.A triangular roof brace has angles of 38° and 67°. Find the third angle. Show your calculation.
4.An isosceles triangle has a vertex angle of 46°. Calculate each of its equal base angles.
Use the clues
Build equations from the information given, then check whether the angles make a triangle.
5.A triangle’s angles are in the ratio 2:3:4. Work out all three angles and classify the triangle by its angles.
6.The angles of a triangle are x°, (x + 20)° and (2x − 10)°. Form an equation and find x and all three angles.
7.A triangle has an exterior angle of 128°. One of the two opposite interior angles is 53°. Find the other opposite interior angle. Explain the angle fact you used.
8.A student says, “A triangle with angles 60°, 70° and 80° is possible because every angle is less than 90°.” Is the student correct? Give a reason.
TrueFalse
9.A right-angled triangle has one acute angle of 34°. Find its other acute angle and explain why the two acute angles have that total.
10.Create a triangle with an exterior angle of 115° and one opposite interior angle of 48°. Draw and label it, then calculate the remaining two interior angles.
3 printable pages
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