the three angles of a triangle are represented by 13 x/3,7x/3,5x/6.find the measure of its obtus angle.

To find the measure of the obtuse angle in a triangle, we need to know the values of all three angles. From the given information, we have the three angles represented by:

Angle 1: 13x/3
Angle 2: 7x/3
Angle 3: 5x/6

The sum of all angles in a triangle is always 180 degrees. So, we can write the equation:

(13x/3) + (7x/3) + (5x/6) = 180

To solve this equation, we need to find the value of x first. Let's simplify the equation:

(13x + 7x + 5x/2) = 180
(26x + 14x + 5x/2) = 180
(57x/2) = 180

Now, we can solve the equation for x:

57x = 360
x = 360/57
x ≈ 6.316

Now that we have the value of x, we can substitute it back into the original expressions for the angles to find their specific values. Let's calculate them:

Angle 1: 13x/3 ≈ (13 * 6.316)/3 ≈ 27.105 degrees
Angle 2: 7x/3 ≈ (7 * 6.316)/3 ≈ 15.047 degrees
Angle 3: 5x/6 ≈ (5 * 6.316)/6 ≈ 5.263 degrees

Now, to determine the obtuse angle, we compare these angles and find the one that is larger than 90 degrees (since an obtuse angle is greater than 90 degrees). We notice that Angle 1 (27.105 degrees) is the largest. Therefore, the obtuse angle is Angle 1.

So, the measure of the obtuse angle in the triangle is approximately 27.105 degrees.

13x/3 + 7x/3 + 5x/6 = 180

multiply each term by 6
26x + 14x + 5x = 1080

solve for x, sub its value into 13x/3