ISEE Upper Level Math : How to find an angle in an acute / obtuse triangle
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Example Questions
Example Question #1 : Acute / Obtuse Triangles
Which of the following is true about a triangle with two angles that measure 
This triangle cannot exist.
This triangle is scalene and obtuse.
This triangle is scalene and right.
This triangle is isosceles and right.
This triangle is isosceles and obtuse.
This triangle cannot exist.
A triangle must have at least two acute angles; however, a triangle with angles that measure 
Example Question #41 : Triangles
Which of the following is true about a triangle with two angles that measure 
The triangle is acute and isosceles.
The triangle is acute and scalene.
The triangle is obtuse and scalene.
The triangle cannot exist.
The triangle is obtuse and isosceles.
The triangle cannot exist.
A triangle must have at least two acute angles; however, a triangle with angles that measure 
Example Question #2 : How To Find An Angle In An Acute / Obtuse Triangle
One angle of an isosceles triangle has measure 
Not enough information is given to answer this question.
An isosceles triangle not only has two sides of equal measure, it has two angles of equal measure. This means one of two things, which we examine separately:
Case 1: It has another 
Case 2: Its other two angles are the ones that are of equal measure. If we let 
Both angles measure
Example Question #2 : Acute / Obtuse Triangles
The angles of a triangle measure 
The sum of the degree measures of the angles of a triangle is 180, so we solve for 
Example Question #3 : Acute / Obtuse Triangles
The acute angles of a right triangle measure 
Evaluate 
The degree measures of the acute angles of a right triangle total 90, so we solve for 
Example Question #4 : Acute / Obtuse Triangles
Note: Figure NOT drawn to scale
Refer to the above figure. 
What is the measure of 
Congruent chords of a circle have congruent minor arcs, so since 
Since there are 
The inscribed angle 
Example Question #5 : Acute / Obtuse Triangles
Solve for 
The sum of the internal angles of a triangle is equal to 
Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle
Refer to the above figure. Express 
The measure of an interior angle of a triangle is equal to 180 degrees minus that of its adjacent exterior angle, so
and
The sum of the degree measures of the three interior angles is 180, so
Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle
In the above figure, 
Give the measure of 
The sum of the degree measures of a triangle is 
Example Question #2 : How To Find An Angle In An Acute / Obtuse Triangle
Figure NOT drawn to scale.
Refer to the above figure. Evaluate 
The measure of an exterior angle of a triangle, which here is 
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