Question

M∠JHI = (2x + 7)°, m∠GHI = (8x - 2)°, and m∠JHG = 65°. Find m∠JHI and m∠GHI.

A. ∠JHI: 47°, ∠GHI: 384°
B. ∠JHI: 38°, ∠GHI: 58°
C. ∠JHI: 55°, ∠GHI: 422°
D. ∠JHI: 62°, ∠GHI: 506°

Answer 1

To find the measure of angles JHI and GHI, we solve the equation (2x + 7)° + (8x - 2)° + 65° = 180°, which results in x being 11°. Therefore, m∠JHI is 29° and m∠GHI is 86°. correct option is B.

Step-by-step explanation:

The problem involves finding the measures of angles JHI and GHI. We know that m∠JHG = 65°, which means that the sum of the measures of angles JHI and GHI must be 180° because they form a straight line with angle JHG. Therefore, we can set up the following equation:

(2x + 7)° + (8x - 2)° + 65° = 180°

To find the value of x, we combine like terms:

10x + 70 = 180

10x = 110

x = 11

Now we can find the measure of angles JHI and GHI:

m∠JHI = (2x + 7)° = (2*11 + 7)° = 29°

m∠GHI = (8x - 2)° = (8*11 - 2)° = 86°

The previous answer given, with m∠JHI being 62° and m∠GHI being 506°, is incorrect as it results in an angle greater than the maximum possible angle in a triangle (180°) and a straight line (also 180°).