ISEE Upper Level Quantitative : How to find an angle

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

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Example Questions

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Example Question #11 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Obtuse

Refer to the above figure. Which is the greater quantity?

(a) 

(b) 

Possible Answers:

(b) is the greater quantity

(a) and (b) are equal

(a) is the greater quantity

It is impossible to determine which is greater from the information given

Correct answer:

(a) is the greater quantity

Explanation:

Extend  as seen in the figure below:

Obtuse

The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles; specifically,

,

and

 

However, , so, by substitution,

Example Question #11 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Given: . Which is the greater quantity?

(a) 

(b) 

Possible Answers:

It is impossible to determine which is greater from the information given

(a) is the greater quantity

(b) is the greater quantity

(a) and (b) are equal

Correct answer:

(b) is the greater quantity

Explanation:

Below is the referenced triangle along with , an equilateral triangle with sides of length 10:

Triangles

As an angle of an equilateral triangle,  has measure . Applying the Side-Side-Side Inequality Theorem, since , and , it follows that , so .

Also, since , by the Isosceles Triangle Theorem, . Since , and the sum of the measures of the angles of a triangle is , it follows that

Substituting and solving:

.

 

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