In a triangle, the measure of the first angle is 24 degrees more than the measure of the second angle. The measure of the third angle is four times the measure of the second angle. If the total number of degrees in a triangle is 180, what is the measure of the largest angle?

Triangle is the polygon with three edges, three vertices and three angle. The total number of degrees in a triangle is always 180 degrees. The value of the largest angle in the given triangle is 104 degrees.

Given-

Let The measure of the second angle is x degrees.

The measure of the first angle is 24 degrees more than the measure of the second angle. Thus first angle is (24+x) degrees.

The third angle is four times the measure of the second angle. Thus the measure of the third angle is 4x.

What is triangle?

Triangle is the polygon with three edges, three vertices and three angle. The total number of degrees in a triangle is always 180 degrees.

As we know that the sum of the all the three angle in the triangle is 180 degrees. Therefore,

[tex](24+x)+x+4x=180[/tex]

[tex]6x=124-48[/tex]

[tex]6x=156[/tex]

[tex]x=\dfrac{156}{6}[/tex]

[tex]x=26[/tex]

Hence the the measure of the second angle is 26 degrees. Now The measure of the first angle is 24 degrees more than the measure of the second angle. Thus,

[tex]=24+26[/tex]

[tex]=50[/tex]

Hence measure of the first angle is 50 degrees. Now the third angle is four times the measure of the second angle. Thus,

[tex]=4\times 26=104[/tex]

Hence, the measure of the third angle is 104 degrees.

Thus the value of the largest angle in the given triangle is 104 degrees.

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