ISEE Upper Level Math : How to find an angle in an acute / obtuse triangle

Study concepts, example questions & explanations for ISEE Upper Level Math

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Example Questions

Example Question #1 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

Exterior_angle

Note: Figure NOT drawn to scale.

What is the measure of angle 

Possible Answers:

Correct answer:

Explanation:

The two angles at bottom are marked as congruent. One forms a linear pair with a  angle, so it is supplementary to that angle, making its measure .  Therefore, each marked angle measures .

The sum of the measures of the interior angles of a triangle is , so:

Example Question #11 : How To Find An Angle In An Acute / Obtuse Triangle

Which of the following is true about a triangle with two angles that measure  and ?

Possible Answers:

This triangle is scalene and right.

This triangle is scalene and obtuse.

This triangle is isosceles and obtuse.

This triangle cannot exist.

This triangle is isosceles and right.

Correct answer:

This triangle cannot exist.

Explanation:

A triangle must have at least two acute angles; however, a triangle with angles that measure  and  could have at most one acute angle, an impossible situation. Therefore, this triangle is nonexistent.

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