Q1.
Construct a triangle ABC where AB = 5 cm, ∠A = 45° and ∠B = 80°.
Answer The two arms drawn at 45° and 80° meet at C, the third vertex.
Take the given side AB as the base and grow both angles from it.
- Step 1: Draw the base AB of length 5 cm.
- Step 2: Draw ∠A and ∠B of measures 45° and 80° respectively, on the same side of AB.
- Step 3: The point of intersection of the two new line segments is the third vertex C.
Third angle ∠C = 180° – (45° + 80°)
= 180° – 125°
= 55°
= 180° – 125°
= 55°
Why it happens: The two arms lean towards each other because 45° + 80° = 125° is less than 180°. Leaning arms are bound to meet, and where they meet is the only possible third vertex — so again there is exactly one triangle.