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 the measure of the vertex is
_°.
If the exterior angle of the vertex is 150°, then the measure of the angle of each base is
_° and the measure of the vertex is
_°.
Ext.Ang.Bases = 150
Int.Ang.Bases = 180-150 = 30 each
For whole triangle: 30+30+x = 180
Int.Ang.Vrtx. = x = 120
Ext.Ang.Vrtx. = 150
Int.Ang.Vrtx. = 180 - 150 = 30
Int.Ang.Bases = 180 - 30 = 150
Base angles are 0.5×150 = 75 each
To find the measures of the angles of an isosceles triangle given an exterior angle, we can use the following steps:
Step 1: Recall that the sum of the angles in any triangle is 180°.
Step 2: Identify the base angles and the vertex angle of the triangle.
Step 3: Find the measure of the base angles using the fact that the base angles of an isosceles triangle are congruent.
Step 4: Use the given exterior angle to find the measure of the vertex angle.
Let's apply these steps to find the measures of the angles in an isosceles triangle with an exterior angle of 150°.
Case 1: Exterior angle at the bases = 150°
In this case, the exterior angle is formed by extending one of the base angles.
Step 1: The sum of the angles in any triangle is 180°.
Step 2: Let's label the base angles as x° each, and the vertex angle as y°.
Step 3: Since the base angles are congruent in an isosceles triangle, the sum of the base angles = 2x°.
Step 4: The exterior angle is formed by extending one of the base angles, so the sum of the exterior angle and the adjacent interior angle = 180°. Therefore, (2x° + 150°) = 180°.
Solving the equation, we have:
2x° + 150° = 180°
2x° = 180° - 150°
2x° = 30°
x° = 15°
Hence, the measure of each base angle is 15° and the measure of the vertex angle is y°.
Case 2: Exterior angle at the vertex = 150°
In this case, the exterior angle is formed by extending the vertex angle.
Step 1: The sum of the angles in any triangle is 180°.
Step 2: Let's label the base angles as x° each, and the vertex angle as y°.
Step 3: Since the base angles are congruent in an isosceles triangle, the sum of the base angles = 2x°.
Step 4: The exterior angle is formed by extending the vertex angle, so the sum of the exterior angle and the adjacent interior angle = 180°. Therefore, (x° + 150°) = 180°.
Solving the equation, we have:
x° + 150° = 180°
x° = 180° - 150°
x° = 30°
Hence, the measure of each base angle is x° = 30° and the measure of the vertex angle is y°.
Therefore, the two possible sets of measures for the angles of the isosceles triangle are:
Case 1: Exterior angle at the bases = 150°
- Each base angle measures 15°
- The vertex angle measure is y°
Case 2: Exterior angle at the vertex = 150°
- Each base angle measures 30°
- The vertex angle measure is y°
An exterior angle of an isosceles triangle has measure 130 . Find two possible sets of measures for the angles of the triangle
noooo
exterior + interior = 180
The interior angle could be either
the vertex angle
or one of the two base angles
An exterior angle of an isosceles triangle has measure 110degrees. Find two possible sets of measures for the angles of the triangle.
If the exterior angle of the bases is 160degrees, then the measure of the angle of each base is
nothingdegrees and the measure of the vertex is
nothingdegrees.