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AQA GCSE · Question 06.3 · Geometry and Measures
Three straight lines intersect as shown. What type of triangle is made? You must show your working.
Three straight lines intersect as shown. What type of triangle is made? You must show your working.
How to approach this question
1. Identify the triangle formed by the intersecting lines.
2. Use angle rules to find the angles inside the triangle.
3. The angle vertically opposite to the given 47° angle is one angle of the triangle.
4. The angle vertically opposite to the given 86° angle is another angle of the triangle.
5. Use the fact that angles in a triangle sum to 180° to find the third angle.
6. Compare the three angles of the triangle.
7. If two angles are equal, the triangle is isosceles. If all three are different, it is scalene. If one is 90°, it is right-angled. If all are 60°, it is equilateral.
Full Answer
Isosceles.
Working:
Angle vertically opposite to 86° is also 86°.
Angle vertically opposite to 47° is also 47°.
The third angle in the triangle is 180° - 86° - 47° = 47°.
Since two angles are equal (47°), the triangle is isosceles.
1. **Find angles inside the triangle:**
The angles inside the central triangle are vertically opposite to the angles given outside. Vertically opposite angles are equal.
So, one angle in the triangle is 47°.
Another angle in the triangle is 86°.
2. **Find the third angle:**
The sum of angles in a triangle is 180°.
Third angle = 180° - (47° + 86°)
Third angle = 180° - 133°
Third angle = 47°
3. **Classify the triangle:**
The angles of the triangle are 47°, 86°, and 47°.
Since two of the angles are equal, the triangle is an **isosceles** triangle. (An isosceles triangle has two equal angles and two equal sides).
Common mistakes
✗ Using the wrong angle rules (e.g., angles on a straight line).
✗ Incorrectly calculating the third angle.
✗ Knowing the angles but giving the wrong triangle type (e.g., scalene).
✗ Not providing working to justify the answer.
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