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One of the angles of an isosceles triangle is 80 degrees. All the angles of the triangle are greater than 40 degrees. At what time between 4 and 5 will the angle between hour hand and minute hand is same as the other angle of the triangle?

One of the angles of an isosceles triangle is 80 degrees. All the angles of the triangle are greater than 40 degrees. At what time between 4 and 5 will the angle between hour hand and minute hand is same as the other angle of the triangle? Correct Answer (30 +10/11) past 4

In isosceles triangle, two angles are equal. Let the angle be x

Case 1:

x + x + 80 = 180

x = 50 degrees

Case 2 :

80 + 80 + x = 180

X = 20 degrees

As all the angles of the triangle are greater than 40 degrees. Case 2 gets eliminated.

So, angle between hour hand and minute hand should be 50 degrees.

The formula for finding the angle between the hour hand and minute hand is

Angle between the hands = 11 × m/2 – 30 H

m denotes the minute hand and H denotes the hour hand

Angle = 50       H = 4

50 = 11 × m/2 – 30 × 4

m = 340/11 = (30 + 10/11)

Hence, the time is (30 + 10/11) minutes past 4.

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