The measure of the vertex angle in an isosceles triangle is six less than four time the measure of the base angle. find the meas

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nata0808

3 months ago

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The measure of the vertex angle in an isosceles triangle is six less than four time the measure of the base angle. find the meas

ure of the vertex angle

Mathematics

1 answer:

Svet_ta [12.7K] · Answer 1 · 2026-02-22T03:00:14+03:00

An isosceles triangle is characterized by having two equal-length sides. Therefore, the two angles at the base must also be equal. Given that the sum of the internal angles in a triangle is 180°, we can express the general equation as

180° = 2*Base angle + Vertex angle

Let’s denote the base angle as x. Consequently, the vertex angle can be expressed as
Vertex angle = 4x - 6
Substituting this in, we have:
180 = 2x + 4x - 6
Solving for x yields:
x = 31°

So, the vertex angle equals 4(31°) - 6
Vertex angle = 118°