Question

In ΔHIJ, m, angle, H, equals, left bracket, 4, x, minus, 9, right bracket, degreesm∠H=(4x−9)

∘
, m, angle, I, equals, left bracket, 3, x, minus, 17, right bracket, degreesm∠I=(3x−17)
∘
, and m, angle, J, equals, left bracket, 3, x, plus, 16, right bracket, degreesm∠J=(3x+16)
∘
. Find m, angle, J, .m∠J.

Answer 1

To find m∠J in triangle HIJ, we use the fact that the sum of angles in a triangle is 180° to form an equation with the given expressions for each angle. After solving for x, we substitute it back into the expression for m∠J and find that m∠J equals 73°.

Step-by-step explanation:

The student is asked to find m∠J in triangle HIJ, given the expressions for angles H, I, and J in terms of x. Since the sum of angles in any triangle is 180°, we can write an equation that represents this fact:

m∠H + m∠I + m∠J = 180°

Plugging in the given expressions for m∠H, m∠I, and m∠J, we have:

(4x - 9) + (3x - 17) + (3x + 16) = 180

Simplifying, we can combine like terms:

10x - 10 = 180

Now, we solve for x:

10x = 190

x = 19

Finally, to find m∠J, we substitute x back into the expression for m∠J:

m∠J = (3x + 16)

m∠J = (3(19) + 16)

m∠J = (57 + 16)

m∠J = 73°