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Question

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A searchlight rotates through one complete revolution every 16 seconds. How long does it take the light to rotate through 90°?

is it 1440 seconds

this problem please tell me how to do this problem

An isosceles triangle is a triangle in which two sides are equal in length. The angle between the two equal sides is called the vertex angle, while the other two angles are called the base angles. If the vertex angle is 50°, what is the measure of the base angles?

Answer 1

A circle consists of 360 degrees.  If the searchlight rotates 90 deg., then it goes through 90/360 of the circle.  Multiply this number by the time it takes to make one revolution, and ta-da!

Next:

All triangles' angles add up to 180 deg.  The base angles of an isosceles triangle are equal.  So,

50 + base angle + base angle = 180.

Or,

50 + 2 x base angle = 180.

Can you take it from here?

Answer 2

90 degrees is 1/4 of one revolution so it would take 1/4 the time of one revolution to go 90 degrees.  Tip: it is not 1440 seconds

the base angles will be the same as each other and all three angles will add up to 180 degrees