Question

In a triangle the measure of the first angle is 24 degrees more than 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?

Answer 1

The greatest angle in the given triangle is 104 degrees.

What is a triangle?

• The polygon with 3 sides, three vertices, and three angles is known as a triangle.
• A triangle's overall number of degrees is always 180 degrees.

Given:

• Let, the second angle has a measurement of x degrees.
• The first angle's measurement is 24 degrees greater than the second angle's measurement.
• As a result, the first angle is (24+x) degrees.
• The third angle is four times as large as the second.
• As a result, the third angle has a measure of 4x.

So,

• (24 + x) + x + 4x = 180
• 6x = 124 - 48
• 6x = 156
• x = 156/6
• x = 26

As a result, the second angle has a measurement of 26 degrees.

The first angle's measurement is now 24 degrees greater than the second angle's measurement.

Now,

• = 24 + 26
• = 50

As a result, the first angle has a measure of 50 degrees.

The third angle is now four times the size of the second angle.

So,

• 4 × 26 = 104

Therefore, the greatest angle in the given triangle is 104 degrees.

Know more about triangles here:

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