High School Math : How to find an angle in an acute / obtuse triangle
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Example Questions
Example Question #24 : Acute / Obtuse Triangles
A triangle has angles that measure 
The sum of the angles of any triangle is always 
Sum of the two given angles: 
Difference between 
Example Question #1 : Acute / Obtuse Triangles
In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?
A (Angle A = 41°)
B C
41
98
90
82
98
If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:
41° + 41° = 82°
Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:
180° - 82° = 98°
Example Question #327 : Geometry
You are given a triangle with angles 
Recall that the sum of the angles of a triangle is 
We combine the like terms on the left.
Subtract 
Thus, we have that our missing angle is 
Example Question #51 : Triangles
What is the third angle in a triangle with angles of 
No such triangle can exist.
No such triangle can exist.
We know that the sum of the angles of a triangle must add up to 
Example Question #21 : Acute / Obtuse Triangles
Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.
60°
80°
70°
50°
50°
To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.
Example Question #1 : Acute / Obtuse Isosceles Triangles
If the average (arithmetic mean) of two noncongruent angles of an isosceles triangle is 
Since the triangle is isosceles, we know that 2 of the angles (that sum up to 180) must be equal. The question states that the noncongruent angles average 55°, thus providing us with a system of two equations:
Solving for x and y by substitution, we get x = 70° and y = 40° (which average out to 55°).
70 + 70 + 40 equals 180 also checks out.
Since 70° is not an answer choice for us, we know that the 40° must be one of the angles.
Example Question #2 : Acute / Obtuse Triangles
Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is 
Find the measure of 
The measure of 
Because the measures of the three angles in a triangle must add up to 
Example Question #2 : Acute / Obtuse Isosceles Triangles
The base angle of an isosceles triangle is 
Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Solve the equation 
x = 180 - 27 - 27
x = 126
Therefore the measure of the vertex angle is 
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