Question

The measures of the three angles of a triangle are given by 18x − 7, 12x + 9, and 4x. What is the measure of the largest angle?

Answer 1

Answer:

The greatest angle is $18x-7$

Explanation:

According to angle sum property of a triangle, sum of all the angles of a triangle is equal to $180$°.

The given angles of a triangle are $18x-7,12x+9,4x$

Therefore,

$18x-7+12x+9+4x=180$°

$34x+2=180$°

$34x=178$°

$x=\frac{178}{34}=\frac{89}{17}$

$18x-7=18(\frac{89}{17})-7=\frac{1602-119}{17}=\frac{1483}{17}$≈ 87.2°

$12x+9=12(\frac{89}{17})+9=\frac{1068+153}{17}=\frac{1221}{17}$ ≈ 71.8°

$4x=4(\frac{89}{17})=\frac{356}{17}$ ≈ 20.9°

Therefore, greatest angle is $18x-7$