Final answer:
To find the measure of angle zh, we use the fact that angles zh and zg are complementary. By setting up an equation with zg as twice zh plus six, we solve for zh and find that m zh is 28 degrees.
Step-by-step explanation:
The given problem states that the measure of angle zg is six more than twice the measure of angle zh. If angle lg and lh are complementary angles, to find m zh we will need to use the definition of complementary angles and set up an equation to solve for zh.
Let's assume that m zh = x. Since complementary angles add up to 90 degrees, we have:
m zh + m zg = 90
According to the problem, m zg is twice m zh plus six, therefore:
x + 2x + 6 = 90
Now, solving for x:
3x + 6 = 90
3x = 84
x = 28
Therefore, the measure of angle zh is 28 degrees.