Final answer:
To calculate the measure of angle FGJ, set the provided expressions equal since GH bisects the angle and solve for 'x'. Substitute 'x' back into the expression for the angle FGJ to get the measure of 60°.
Step-by-step explanation:
The question asks to find the measure of angle FGJ given that line GH bisects it and provides expressions for the measures of angles FGH and HGJ. First, establish that the measure of angle FGJ is the sum of the measures of angles FGH and HGJ since GH bisects angle FGJ. We are given that m∠FGH = 5x + 20° and m∠HGJ = 3x + 24°. To find the measure of angle FGJ, add the expressions: m∠FGJ = m∠FGH + m∠HGJ = (5x + 20°) + (3x + 24°). Simplify this to 8x + 44°. Since GH bisects angle FGJ, the two angles FGH and HGJ are equal, thus their expressions must also be equal. Set them equal to each other: 5x + 20° = 3x + 24°. Solving for x gives 2x = 4° and x = 2°. Substitute x back into the expression for m∠FGJ:
m∠FGJ = (5(2°) + 20°) + (3(2°) + 24°) = (10° + 20°) + (6° + 24°) = 60°.