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 #51 : Triangles

Exterior_angle

Note: Figure NOT drawn to scale.

What is the measure of angle \(\displaystyle y?\)

Possible Answers:

\(\displaystyle y = 152\)

\(\displaystyle y = 142\)

\(\displaystyle y = 134\)

\(\displaystyle y = 124\)

\(\displaystyle y = 129\)

Correct answer:

\(\displaystyle y = 124\)

Explanation:

The two angles at bottom are marked as congruent. One forms a linear pair with a \(\displaystyle 152 ^{\circ }\) angle, so it is supplementary to that angle, making its measure \(\displaystyle (180-152)^{\circ } = 28^{\circ }\).  Therefore, each marked angle measures \(\displaystyle 28^{\circ }\).

The sum of the measures of the interior angles of a triangle is \(\displaystyle 180^{\circ }\), so:

\(\displaystyle y + 28 + 28 = 180\)

\(\displaystyle y +56= 180\)

\(\displaystyle y +56-56 = 180-56\)

\(\displaystyle y = 124\)

Example Question #91 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Which of the following is true about a triangle with two angles that measure \(\displaystyle 120^{\circ }\) and \(\displaystyle 90^{\circ }\)?

Possible Answers:

This triangle is scalene and right.

This triangle cannot exist.

This triangle is isosceles and right.

This triangle is scalene and obtuse.

This triangle is isosceles and obtuse.

Correct answer:

This triangle cannot exist.

Explanation:

A triangle must have at least two acute angles; however, a triangle with angles that measure \(\displaystyle 120^{\circ }\) and \(\displaystyle 90^{\circ }\) could have at most one acute angle, an impossible situation. Therefore, this triangle is nonexistent.

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