The measures of the angles of a triangle are in the ratio 2 : 3 : 4. The simplified ratio of the measures of the exterior angles of the triangle is a : b : c. Find a + b + c.

18

Step-by-step explanation:

The measures of the angles of a triangle are in the ratio 2:3:4 means we have one interior angle measuring 2x, another measuring 3x, and the last one measuring 4x. We know the sum of the measures of the interior angles of a triangle is 180 degrees.

We need to solve the following equation to find first x, and then find the measurement of each interior angle of the triangle.

2x+3x+4x=180

(2+3+4)x=180

(9)x=180

x=180/9

x=20

So one interior angle measures 2x=2(20)=40.

Another measures 3x=3(20)=60.

The last measuring 4x=4(20)=80.

The exterior angles of this triangle therefore measure the following:

180-40=140

180-60=120

180-80=100

So the un-simplified ratio of the measures of the exterior angles is as follows:

140:120:100.

Let's simplify that.

It is easy to see each number is divisible by 10.

Let's reduce it by dividing each by 10:

14:12:10

Let's simplify more (as we want the most simplified ratio).

Each number is divisible by 2 since they are all even.

Let's reduce again but not by dividing by 2:

7:6:5

So the simplified ratio of the measures of the exterior angles of the triangle is a:b:c=7:6:5 and so a+b+c=7+6+5=18.

Answer is 18.

the distance from any point on the parabola to the focus is the exact same as the distance from that point to the directrix.

if you could provide answer choices that might allow me to answer the question easier if my above answer isn't an option! (:

answer: c i think

step-by-step explanation: