High School Math : How to find an angle in an acute / obtuse triangle
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Example Question #21 : How To Find An Angle In An Acute / Obtuse Triangle
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 : How To Find An Angle In An Acute / Obtuse Triangle
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 #51 : Triangles
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 #171 : Act Math
Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.
50°
60°
70°
80°
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 #439 : Geometry
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 #1421 : Concepts
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 #440 : Geometry
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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