The ratio of the measure of the vertex angle is to the base angle of an isosceles triangle is 8:5 than the measure of the vertex angle is [tex]80^\circ[/tex].
Given :
The ratio of the measure of the vertex angle is to the base angle of an isosceles triangle is 8:5.
Solution :
An isosceles triangle has two equal sides. This property gives two angles of the triangle to be equal. Let an isosceles triangle ABC.
Now we know that the sum of all three interior angles of an triangle is equal to [tex]180^\circ[/tex].
[tex]\rm \angle A + \angle B+ \angle C = 180^\circ[/tex] --- (1)
Given that the ratio of the measure of the vertex angle is to the base angle of an isosceles triangle is 8:5 therefore equation (1) is as follows:
[tex]8x + 5x +5x = 180^\circ[/tex]
[tex]18x = 180^\circ[/tex]
[tex]x = 10^\circ[/tex]
Therefore, the vertex angle = [tex]8\times 10^\circ = 80^\circ[/tex]
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