Finding Angles - SAT Subject Test in Math I

Card 0 of 5

Question

What angle do the minute and hour hands of a clock form at 4:45?

Answer

There are twelve numbers on a clock; from one to the next, a hand rotates . At 4:45, the minute hand is exactly on the "9" - that is, at the . The hour hand is three-fourths of the way from the "4" to the "5" - that is, on the position. Therefore, the difference is the angle they make:

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Question

What angle do the minute and hour hands of a clock form at 8:50?

Answer

There are twelve numbers on a clock; from one to the next, a hand rotates . At 8:50, the minute hand is exactly on the "10" - that is, on the position. The hour hand is five-sixth of the way from the "8" to the "9" - that is, on the position. Therefore, the difference is the angle they make:

.

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Question

Hexagon

Note: Figure NOT drawn to scale.

The above hexagon is regular. What is ?

Answer

Two of the angles of the quadrilateral formed are angles of a regular hexagon, so each measures

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The four angles of the quadrilateral are . Their sum is , so we can set up, and solve for in, the equation:

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Question

Can a triangle have a set of angles that are and degrees?

Answer

A triangle's angles must add up to degrees.

The angles given add up to 181,

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That means that this cannot be an actual triangle.

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Question

If two angles of a triangle are and , find the measurement of the third angle.

Answer

Step 1: Recall the sum of the angles of a triangle...

The sum of the internal angles of a triangle is .

Step 2: To find the missing angle, subtract the given angles from ...

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