ACT Math : How to find an angle in a quadrilateral

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Find An Angle In A Quadrilateral

The interior angles of a quadrilateral are , and . What is the measure of the smallest angle?

Possible Answers:

Correct answer:

Explanation:

The key piece of knowledge is that the interior angles of a quadrilateral add up to .

Therefore, the following equation can be set up:

When we combine like terms, we get:

We then subtract 71 from both sides:

and then divide both sides by 17:

It should be noted that the problem is not finished. The question asks for the measure of the smallest angle. We have only found . If students do not read the question carefully, they may end up selecting  as their answer, which would be incorrect.

The smallest angle will either be  or . To find out, simply plug in  for :

Because , the measure of the smallest angle is .

Example Question #2 : How To Find An Angle In A Quadrilateral

Q6

 bisects . If  then, in degrees, what is the value of ?

Possible Answers:

Correct answer:

Explanation:

A rectangle has two sets of parallel sides with all angles equaling 90 degrees. 

Since  bisects  into two equal parts, this creates an isosceles triangle .

Therefore . The sum of the angles in a triangle is 180 degrees.

Therefore 

Example Question #3 : How To Find An Angle In A Quadrilateral

Q8

The rhombus above is bisected by two diagonals.

If  and  then, in degrees, what is the value of the ?

Note: The shape above may not be drawn to scale. 

Possible Answers:

Correct answer:

Explanation:

A rhombus is a quadrilateral with two sets of parallel sides as well as equal opposite angles. Since the lines drawn inside the rhombus are diagonals,  and  are each bisected into two equal angles.

Therefore,  , which creates a triangle in the upper right quadrant of the kite. The sum of angles in a triangle is 180 degreees.

Thus,

 

Since  is only half of ,

Example Question #191 : Quadrilaterals

Q10

If  and , then, in degrees, what is the value of ?

 

Note: The figure may not be drawn to scale. 

Possible Answers:

Correct answer:

Explanation:

In a rhombus, opposite angles are equal to each other. Therefore we can set  and  equal to one another and solve for :

Therefore,

A rhombus, like any other quadrilateral, has a sum of angles of 360 degrees.

 

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