Q1.
Construct triangles for the following measurements: (a) 75°, 5 cm, 75° (b) 25°, 3 cm, 60° (c) 120°, 6 cm, 30°
Answer
Draw the given side as the base and set the two given angles at its two ends.
| Set | Base | Angles at the ends | Sum of the two angles | Third angle | Type |
|---|---|---|---|---|---|
| (a) 75°, 5 cm, 75° | 5 cm | 75° and 75° | 150° | 30° | Isosceles, acute-angled |
| (b) 25°, 3 cm, 60° | 3 cm | 25° and 60° | 85° | 95° | Scalene, obtuse-angled |
| (c) 120°, 6 cm, 30° | 6 cm | 120° and 30° | 150° | 30° | Isosceles, obtuse-angled |
Third angle = 180° – (sum of the two given angles)
(a) 180° – 150° = 30°
(b) 180° – 85° = 95°
(c) 180° – 150° = 30°
(a) 180° – 150° = 30°
(b) 180° – 85° = 95°
(c) 180° – 150° = 30°
Why it happens: Each sum is less than 180°, so in every case the two arms lean towards each other and must meet. In (c) the third angle equals one of the given angles (30°), which is why that triangle turns out isosceles.
Check it yourself: Measure the third angle with a protractor after construction and compare it with the value in the table.