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Question
In a isoceles traingle each base angle is 30' greater than the vertical angle . Find the measure of all the three angles of the triangles.
In a isoceles traingle each base angle is 30' greater than the vertical angle . Find the measure of all the three angles of the triangles.
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Solution
Notice that in an isosceles triangle there are at least two congruent angles. Also, as in all triangles, the sum of the angles is 180°.
If we say the vertex angle is x°, we can say that each base angle is (x+30)°. We know that the angles' sum is 180°, so we can write the following equation relating each of the angles:
x+(x+30)+(x+30)=180
We can then solve for x and determine that 3x+60=180, which leads to 3x=120 and finally x=40, so the vertex angle is 40° and each base angle is 70°.
Notice that in an isosceles triangle there are at least two congruent angles. Also, as in all triangles, the sum of the angles is 180°.
If we say the vertex angle is x°, we can say that each base angle is (x+30)°. We know that the angles' sum is 180°, so we can write the following equation relating each of the angles:
x+(x+30)+(x+30)=180
We can then solve for x and determine that 3x+60=180, which leads to 3x=120 and finally x=40, so the vertex angle is 40° and each base angle is 70°.
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