Can You Work Out The Angles In This Triangle?

Consider the unknown angles as 'x'
Therefore, 4:7:9 becomes 4x: 7x: 9x.
Since, the sum of the angles of a triangle is 180°,
4x + 7x + 9x = 180°
20x = 180° (add the like terms)
x = 180° ÷ 20
x = 9
Therefore, by sustituting the value of x, we get,
4(9) : 7(9) : 9(9) = 36:63:81
In this triangle, the smallest angle is 36 and largest one is 81.
Therefore, sum of these angles = 36 + 81 = 117
Thus the problem is solved!

Assume the 3 angles are 4X, 7X and 9X (4+7+9)x=180 x=9 (4+9)*9=117

$\frac{a}{4}$ + $\frac{b}{7}$ + $\frac{c}{9}$ = $\frac{a+b+c}{4+7+9}$ = $\frac{180}{20}$ = 9 --->a= $4 \times 9$ =36 ; c= $9 \times 9$ = 81. So my answer is "" 36+81=117"" .

4x + 7x + 9x = 180 (Angle sum property of triangle)

x=9

4x=4*9=36 (Substituting 9 to x)

9x=9*9=81(Substituting 9 to x)

SUM= 117

Given that the ratio of the angles are $4:7:9$ , so let us take the angles as $4x,7x$ and $9x$ .

Now, we know that sum of all the angles of a triangle is $180°$ .

So, $4x+7x+9x=180 \implies 20x=180 \implies x=9$ .

Now, Sum of the smallest and largest angles $=4x+9x=13x=13\times 9=\boxed{117}$

4x+7x+9x=180 => x=9 13x=13*9=117.

the sum of 4 ,7 and 9 will be 20. as we know the total interior angle of a triangle is 180 degree divide 180 degree by 20 and u will get the value of one part. then total up the product 4 and 9 and the product of 9 and 9 u will get the answer 117

4+7+9=20

4/20 * 180=36

9/20 * 180=81

36+81=117

4x, 7x, and 9x are the measures. That means that x is worth 180/20 = 9. So the largest and smallest add up to 13x, so that means 9x13 = 117

Three angles of a triangle are in a ratio of 4:7:9.

let the ratio be x

4x + 7x + 9x = 180 (the sum of all the three angles in a triangle is 180 )

20x = 180

x = 9

the first angle = 4x = 36

the second angle = 7x =63

the third angle = 9x =81

the sum of the smallest and the largest angle of the triangle. = 36 + 81 = 117

let the common multiple be x so 4x +7x+9x = 180 x=9 therefore angles are 36 63 n 81 so ans is 117.

The sum of ratios of the sides is 4 + 7 + 9 = 20.

The smallest angle is $\frac{4}{20}$ * 180 = 36 since 180 is the sum of interior angles of a triangle.

The largest angle is $\frac{9}{20}$ * 180 = 81

Hence,the sum of the smallest and largest angle is 36 + 81 = 117 degrees.

If we have the ratio 4:7:9 and that the sum is 180, so there is a number n that satisfy: 4n+7n+9n=180, n=9, the largest angle is 81, and the smallest is 36. In this way, we have the sum 117.

Let 4x+7x+9x = 180 20x=180 x=9 The smallest angle = 4x9 = 36 The largest angle = 9x9 = 81 The sum of smallest and largest angle = 36 + 81 = 117

The sum of all angles in a triangle must always equal 180°, so by adding up the ratios (4+7+9) to get a total of 20 and dividing the total internal angles of the triangle (180/20=9) we know what the ratio of each angle is (36:63:81). Then we just add up the largest and smallest values (36+81=117).

The sum of the three angles of a triangle is 180. Because the ratio of the 3 angles is 4:7:9 and we need to find the sum of the smallest and the largest angle then the sum should be equal to 180.(4+9)/20=117

You have to represent each element by 'x' then add and equate to 180. 4X + 7X + 9X = 180 20X = 180 X = 9 then substitute '9' to the X of 4 and the X of 9 multiply and then add. 4(9) + 9(9) 36 + 81 = 117

Triangle has 180 degrees of angles. So... we must know if 4 : 7 : 9 = 4x : 7x : 9x ---> So, the sum of the smallest and the largest angle of the triangle = (4x + 9x)/(4x + 7x + 9x) * 180 = 13x/20x * 180 = 13/20 * 180 = 9 * 13 = 117 Degrees. ANSWER : 117