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?
26 degrees
50 degrees
104 degrees
136 degrees

Here goes the answer. Hope it helps.

Measure of largest angle in a triangle is equals to 104 degrees.

" Triangle is a 2 dimensional geometrical figure which has three sides and three vertices. Sum of all the angles of triangle is equals to 180°."

According to the question,

x represents the measure of first angle

y represents the measure of second angle

z represents the measure of third angle

Situation 1: First angle is 24 degree more than second angle , it represents the equation:

x = 24 + y               ____(1)

Situation 2: Third angle is four times the measure of second angle, it represents the equation:

z = 4y                       ___(2)

Situation 3: Total number of degree in a triangle is 180, it represents the equation :

x + y + z = 180°           ____(3)

Substitute the value of (1) and (2) in (3) we get,

24 + y + y + 4y = 180°

⇒ 6y + 24 = 180°

⇒ 6y = 180 - 24

⇒ 6y = 156

⇒ y = 26degrees

Therefore,

x = 24 + 26

  = 50 degrees

z = 4 × 26

  = 104 degrees

Hence, measure of largest angle in a triangle is equals to 104 degrees.

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