Q1.
Can you draw a pair of intersecting lines such that all four angles are equal? Can you figure out what will be the measure of each angle?
Answer
Yes, and each angle must be 90°.
∠a + ∠b + ∠c + ∠d = 360° (a full turn)
All four are equal, say each = x
4x = 360°
x = 360° ÷ 4 = 90°
All four are equal, say each = x
4x = 360°
x = 360° ÷ 4 = 90°
Why it happens: The four angles fill up the complete turn around the crossing point, which is 360°. Sharing 360° equally among four angles gives 90° each — a right angle.
Lines that cross like this are called perpendicular lines. In Fig. 5.4, lines l and m are perpendicular to each other. The right angle is shown by a small square, not by an arc.
Check it yourself: The corner of a page, the corner of your desk and the two edges of a set square are all perpendicular pairs. Slide the corner of a page into the crossing — if it fits exactly, the lines are perpendicular.