Question

The sum of the angles of a triangle is 180 degrees. The second angle is 40 degrees more than the first

angle and the third angle is 5 times the measure of the first angle. What is the measure of the largest
angle?

Answer 1

`\huge{\purple{\underline{\underline{\bf{\pink{ANSWER:-}}}}}}`

• First angle = x

• Second angle = x + 40

• Third angle = 5x

`:\implies\bf{x + x + 40 + 5x = 180} \\ \\ :\implies\bf{7x + 40 = 180} \\ \\ :\implies\bf{7x = 180 - 40} \\ \\ :\implies\bf{7x = 140} \\ \\ :\implies\bf{x = (140)/(7) } \\ \\ :\implies\bf{x = 20}`

The largest angle above is 5x thus,

`:\implies\bf{5x} \\ \\ :\implies\bf{5 * 20} \\ \\ :\implies\bf{100^°}`

Answer 2

100⁰

Explanation:

Let,

First angle = x

Second angle = x + 40

Third angle = 5x

=> x + x + 40 + 5x = 180

=> 7x + 40 = 180

=> 7x = 180 - 40

=> 7x = 140

=> x = 140/7

=> x = 20

Largest angle = 5x = 5(20) = 100⁰