Question

Prove that AOB is a line in the given attachment.

Answer 1

Hi pupil here's your answer ::

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✔We no that sum of all the angles around a point is equal to 360°

so <AOC + <BOC +<BOD+<AOD= 360°

▶x+y+w+z= 360°

▶x+y+x+y=360° (since it is given there w+z=x+y)

▶2x + 2y = 360°

▶2 (x+y) = 360°

▶x+y = 360°/2

▶x+y = 180°

☝According to Axiom 6.2 the sum of two adjacent angles is 180 degree then the non-common arms of the angles form a line.

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hope that it helps. . . . .