Question

If the angles of a triangle are (x+37), (2x+15) and (3x+8). Find the value of x and the measure of each angle.

Answer 1

Answer:

We know that, According to the Angle Sum Property of a Triangle, Sum of all interior angles is equal to 180°.

Here, the angles given are: ( x + 37 )°, ( 2x + 15 )°, ( 3x + 8 )°

Applying the concept of Angle Sum Property, we get,

⇒ x + 37 + 2x + 15 + 3x + 8 = 180°

⇒ 6x + 60° = 180°

⇒ 6x = 180 - 60 = 120°

⇒ x = 120° / 6 = 20°

Therefore the value of x is 20°.

Measure of Each Angle:

⇒ x + 37 = 20 + 37 = 57°

⇒ 2x + 15 = 2 ( 20 ) + 15 = 40 + 15 = 55°

⇒ 3x + 8 = 3 ( 20 ) + 8 = 60 + 8 = 68°

Therefore the angles are : 57°, 55°, 68°.

Hope it helped you !!

Have a great day :)

Answer 2

Answer:

x=75

Step-by-step explanation:

angles of a triangle are x, x + 15 and 2x - 15

here, we've to find the smallest angle of the triangle.  

so first of all, we needa know the value of x.

we know that, sum of all angles in a triangle = 180°

so we can write,

➡ x + x + 15 + 2x - 15 = 180°

➡ 4x = 180°

➡ x = 180/4

➡ x = 45°

the angles are :-

x = 45°

x + 15 = 60°

2x - 15 = 75°

hence, the smallest angle of the triangle is x=75°