High School Math : How to find an angle in an acute / obtuse isosceles triangle
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Example Questions
Example Question #1 : Isosceles Triangles
An isoceles triangle has a base angle five more than twice the vertex angle. What is the difference between the base angle and the vertex angle?
A triangle has 180 degrees. An isoceles triangle has one vertex angle and two congruent base angles.
Let 
So the equation to solve becomes
So the vertex angle is 
Example Question #1421 : Concepts
Points A and B lie on a circle centered at Z, where central angle <AZB measures 140°. What is the measure of angle <ZAB?
15°
25°
30°
Cannot be determined from the given information
20°
20°
Because line segments ZA and ZB are radii of the circle, they must have the same length. That makes triangle ABZ an isosceles triangle, with <ZAB and <ZBA having the same measure. Because the three angles of a triangle must sum to 180°, you can express this in the equation:
140 + 2x = 180 --> 2x = 40 --> x = 20
Example Question #221 : Act Math
Triangle FGH has equal lengths for FG and GH; what is the measure of ∠F, if ∠G measures 40 degrees?
None of the other answers
40 degrees
100 degrees
70 degrees
140 degrees
70 degrees
It's good to draw a diagram for this; we know that it's an isosceles triangle; remember that the angles of a triangle total 180 degrees.
Angle G for this triangle is the one angle that doesn't correspond to an equal side of the isosceles triangle (opposite side to the angle), so that means ∠F = ∠H, and that ∠F + ∠H + 40 = 180,
By substitution we find that ∠F * 2 = 140 and angle F = 70 degrees.
Example Question #1 : Acute / Obtuse Isosceles Triangles
The vertex angle of an isosceles triangle is 
An isosceles triangle has two congruent base angles and one vertex angle. Each triangle contains 
Example Question #222 : Plane Geometry
In an isosceles triangle the base angle is five less than twice the vertex angle. What is the sum of the vertex angle and the base angle?
Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Let 
and 
So the equation to solve becomes
or
Thus the vertex angle is 38 and the base angle is 71 and their sum is 109.
Example Question #2 : Acute / Obtuse Isosceles Triangles
Sides 
This triangle has an angle of 
Example Question #1 : Isosceles Triangles
An isosceles triangle has a vertex angle that is twenty degrees more than twice the base angle. What is the sum of the vertex and base angles?
40
All triangles contain 
Let 
So the equation to solve becomes 
We get 
Example Question #2 : Isosceles Triangles
If an isosceles triangle has an angle measuring greater than 100 degrees, and another angle with a measuring 
In order for a triangle to be an isosceles triangle, it must contain two equivalent angles and one angle that is different. Given that one angle is greater than 100 degrees: 
Example Question #4 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle
An isoceles triangle has a base angle that is twice the vertex angle. What is the sum of the base and vertex angles?
All triangles have 
Let 
So the equation to solve becomes:
Thus 
The sum of the vertex and one base angle is 
Example Question #281 : Geometry
An isoceles triangle has a vertex angle that is 
Every triangle has 
Let 
So the equation to solve becomes 
Thus the base angles are 
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