Question

If the angle measures of a triangle can be expressed as 4x+6,7x−14, and 48−x, what is the value of the smallest angle measure? A. 14 B. 34 C. 62 D. 84

Answer 1

B. 34 degrees

Explanation:

The interior angles of a triangle=180 degrees.

4x+6+7x-14+48-x = 180 degrees

10x = 180-6+14-48

10x = 140

x = 140/10

x = 14

<1) 4x+6=62 degrees

<2) 7x-14=84 degrees

<3) 48-14=34 degrees

Answer 2

B

Explanation:

the sum of the 3 angle measures in a triangle is 180°

sum the 3 given angles, equate to 180 and solve for x

4x + 6 + 7x - 14 + 48 - x = 180 ← collect like terms on left side

10x + 40 = 180 ( subtract 40 from both sides )

10x + 40 - 40 = 180 - 40 ( simplify both sides )

10x = 140 ( divide both sides by 10 )

x = 14

substitute x = 14 into each of the 3 given angles

4x + 6 = 4(14) + 6 = 56 + 6 = 62°

7x - 14 = 7(14) - 14 = 98 - 14 = 84°

48 - x = 48 - 14 = 34°

The smallest angle measure is 34°