At 5 o'clock the hands of a clock make an obtuse angle and a reflex angle. Find the measure of each of these angles.
Lines & Angles
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Question

At 5 o'clock the hands of a clock make an obtuse angle and a reflex angle. Find the measure of each of these angles.

KnowledgeBoat · Accepted Answer

A clock is a circle of 360°, divided into 12 hours. Therefore, each hour gap represents:

$\dfrac{360^\circ}{12} = 30^\circ$

Obtuse Angle:

At 5 o'clock, there are 5 hour gaps between the hands (from 12 to 5).

∴ 5 x 30° = 150°

Reflex Angle:

This is the larger outer angle between the two hands.

∴ 360° - 150° = 210°

The obtuse angle is 150° and the reflex angle is 210°.

Mathematics