# math

In an isoceles triangle top vertex is twice the of the sum of the base angle.find all the exterior angles of the triangle?

1. 👍 0
2. 👎 0
3. 👁 157
1. If it is an isosceles triangle the two base angles will be equal.

Let the base angle be a, then the vertex angle will be:

180° - 2 a

According to the condition:

Top vertex is twice the of the sum of the base angle:

180° - 2 a = 2 ( a + a )

180° - 2 a = 2 * 2a

180° - 2 a = 4 a Add 2 a to both sides

180° - 2 a + 2 a = 4 a + 2 a

180° = 6 a Divide both sides by 6

180° / 6 = a

30° = a

a = 30 °

So the base angles are 30° and the vertex angle is 180° - 2 * 30° = 180° - 60° = 120 °

Exterior base angle is 360° - 30° = 330°

The exterior vertex angle is 360° - 120° = 240°

1. 👍 0
2. 👎 0
2. I believe exterior angles are 180 - interior angles. Their sum is 360.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Geometry

An isosceles right triangle has an area of 98cm squared. Find the length of each leg. The formula of finding the area of a triangle with one right angle is: (b x h)/2 You know that an isoceles triangles has two equal sides. Those

2. ### math

An isosceles triangle has a base of 20 cm. The vertex angle is 82 . Find the length of Each of the two equal sides of the triangle.

3. ### Geometry

An exterior angle of an isosceles triangle has measure 150°. Find two possible sets of measures for the angles of the triangle. If the exterior angle of the bases is 150°​, then the measure of the angle of each base is _° and

4. ### Geometry

The measure of the vertex angle of an isosceles triangle is 98 degrees What is the measure of a base angle

A trough is 5 meters long, 1 meters wide, and 4 meters deep. The vertical cross-section of the trough parallel to an end is shaped like an isoceles triangle (with height 4 meters, and base, on top, of length 1 meters). The trough

2. ### Maths

The vertical angle of an isosceles triangle is twice the sum of the base angles. Find each angle of the triangle??

3. ### Geometry

Can you help me with Always, Sometimes, Never questions?? I have answered all of these, but I am not sure if they are right. 1. The base angle of an isosceles triangle are acute----Always 2. When the altitude and the median are

4. ### Algebra

Question 1 A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle. A triangle ABC is shown. The base of

1. ### calculus

An isosceles triangle is drawn with its vertex at the origin and its base parallel to the x-axis. The vertices of the base are on the curve 5y=25-x^2 Find the area of the largest such triangle.

2. ### Math

A trough is 8 meters long, 3 meters wide, and 5 meters deep. The vertical cross-section of the trough parallel to an end is shaped like an isoceles triangle (with height 5 meters, and base, on top, of length 3 meters). The trough

3. ### algebra.

problems about angles: Hi. I needed help on some problems for the math section that we are doing in class. I am trying out some problems in my math book, but they prove quite difficult. 1. In a certain parallelogram, if the

4. ### geometry

find the value of x in each triangle: triangle x has 1 angle at 53 degree for value x i got: 63.5 degree is that correct? Classify each triangle. 7. The measures of 2 angles are : 45 degree and 45 degree i got: acute 8. the