Question

HS D Question 5: m∠UHI = (2x + 7)° and m∠GHI = (x - 2)° and m∠JHG = 65°. Find m∠JHI and m∠GHI.

A. m∠JHI = 52°, m∠GHI = 139°
B. m∠JHI = 46°, m∠GHI = 199°
C. m∠JHI = 19°, m∠GHI = 46°
D. None of the other answers are correct.

Answer 1

To find the measures of angles JHI and GHI, you can use the fact that the sum of the angles in a triangle is 180 degrees. By setting up and solving an equation using the given information, you can find the value of x. Then, substitute that value back into the expressions for angles JHI and GHI.

Step-by-step explanation:

To find the measures of angles JHI and GHI, we need to use the fact that the sum of the angles in a triangle is 180 degrees. We know that angle JHG is 65 degrees. Using the given information, we can set up the following equation:

(2x + 7) + (x - 2) + 65 = 180

Simplifying the equation, we have:

3x + 70 = 180

Subtracting 70 from both sides gives:

3x = 110

Dividing both sides by 3 gives:

x = 36.7

Now that we know the value of x, we can substitute it back into the expressions for angles JHI and GHI:

m∠JHI = 2x + 7 = 2(36.7) + 7 = 73.4 + 7 = 80.4 degrees

m∠GHI = x - 2 = 36.7 - 2 = 34.7 degrees