All High School Math Resources
Example Questions
Example Question #1 : Isosceles Triangles
The base angle of an isosceles triangle is 15 less than three times the vertex angle. What is the vertex angle?
Every triangle contains 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Let = vertex angle and = base angle
So the equation to solve becomes .
Example Question #431 : Geometry
The base angle of an isosceles triangle is ten less than twice the vertex angle. What is the vertex angle?
Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Let = vertex angle and = base angle
So the equation to solve becomes
So the vertex angle is 40 and the base angles is 70
Example Question #3 : Isosceles Triangles
The base angle of an isosceles triangle is 10 more than twice the vertex angle. What is the vertex angle?
Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Let = the vertex angle and = the base angle
So the equation to solve becomes
The vertex angle is 32 degrees and the base angle is 74 degrees
Example Question #111 : Plane Geometry
In an isosceles triangle, the vertex angle is 15 less than the base angle. What is the base angle?
Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Let = base angle and = vertex angle
So the equation to solve becomes
Thus, 65 is the base angle and 50 is the vertex angle.
Example Question #161 : Geometry
In an isosceles triangle the vertex angle is half the base angle. What is the vertex angle?
Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Let = base angle and = vertex angle
So the equation to solve becomes , thus is the base angle and is the vertex angle.
Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle
If the average of the measures of two angles in a triangle is 75o, what is the measure of the third angle in this triangle?
40°
50°
75°
65°
30°
30°
The sum of the angles in a triangle is 180o: a + b + c = 180
In this case, the average of a and b is 75:
(a + b)/2 = 75, then multiply both sides by 2
(a + b) = 150, then substitute into first equation
150 + c = 180
c = 30
Example Question #132 : Plane Geometry
Which of the following can NOT be the angles of a triangle?
1, 2, 177
45, 45, 90
30.5, 40.1, 109.4
30, 60, 90
45, 90, 100
45, 90, 100
In a triangle, there can only be one obtuse angle. Additionally, all the angle measures must add up to 180.
Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle
Let the measures, in degrees, of the three angles of a triangle be x, y, and z. If y = 2z, and z = 0.5x - 30, then what is the measure, in degrees, of the largest angle in the triangle?
The measures of the three angles are x, y, and z. Because the sum of the measures of the angles in any triangle must be 180 degrees, we know that x + y + z = 180. We can use this equation, along with the other two equations given, to form this system of equations:
x + y + z = 180
y = 2z
z = 0.5x - 30
If we can solve for both y and x in terms of z, then we can substitute these values into the first equation and create an equation with only one variable.
Because we are told already that y = 2z, we alreay have the value of y in terms of z.
We must solve the equation z = 0.5x - 30 for x in terms of z.
Add thirty to both sides.
z + 30 = 0.5x
Mutliply both sides by 2
2(z + 30) = 2z + 60 = x
x = 2z + 60
Now we have the values of x and y in terms of z. Let's substitute these values for x and y into the equation x + y + z = 180.
(2z + 60) + 2z + z = 180
5z + 60 = 180
5z = 120
z = 24
Because y = 2z, we know that y = 2(24) = 48. We also determined earlier that x = 2z + 60, so x = 2(24) + 60 = 108.
Thus, the measures of the three angles of the triangle are 24, 48, and 108. The question asks for the largest of these measures, which is 108.
The answer is 108.
Example Question #553 : Geometry
Angles x, y, and z make up the interior angles of a scalene triangle. Angle x is three times the size of y and 1/2 the size of z. How big is angle y.
18
36
54
108
42
18
The answer is 18
We know that the sum of all the angles is 180. Using the rest of the information given we can write the other two equations:
x + y + z = 180
x = 3y
2x = z
We can solve for y and z in the second and third equations and then plug into the first to solve.
x + (1/3)x + 2x = 180
3[x + (1/3)x + 2x = 180]
3x + x + 6x = 540
10x = 540
x = 54
y = 18
z = 108
Example Question #2 : How To Find An Angle In An Acute / Obtuse Triangle
In the picture above, is a straight line segment. Find the value of .
A straight line segment has 180 degrees. Therefore, the angle that is not labelled must have:
We know that the sum of the angles in a triangle is 180 degrees. As a result, we can set up the following algebraic equation:
Subtract 70 from both sides:
Divide by 2: