In ΔGHI, m, angle, G, equals, left bracket, x, plus, 16, right bracket, degreesm∠G=(x+16)∘, m, angle, H, equals, left bracket, x, plus, 9, right bracket, degreesm∠H=(x+9)∘, and m, angle, I, equals, left bracket, 7, x, plus, 2, right bracket, degreesm∠I=(7x+2)∘. Find m, angle, G, .m∠G
To find the measure of angle G, you need to set up an equation using the information given in the problem:
m∠G = x + 16
Since the sum of the angles in a triangle is 180 degrees, you can also set up the equation:
m∠G + m∠H + m∠I = 180
Substituting the given angle measures into this equation:
(x + 16) + (x + 9) + (7x + 2) = 180
Adding like terms:
9x + 27 = 180
Subtracting 27 from both sides:
9x = 153
Dividing both sides by 9:
x = 17
Now, substitute this value of x back into the equation for angle G:
m∠G = x + 16 = 17 + 16 = 33
Therefore, m∠G is equal to 33 degrees.
To find the measure of angle G, we need to use the information given in the problem. According to the problem statement:
m∠G = (x + 16)°
However, we do not have additional information about the other angles or any relationships between them in this problem. Hence, we cannot determine the value of x or the measure of angle G without further information.
To find the measure of angle G (m∠G), we need to use the given information about the angles in triangle ΔGHI.
We know that the sum of the angles in a triangle is always 180 degrees. So, we can write the equation:
m∠G + m∠H + m∠I = 180
Substituting the given expressions for each angle, we have:
(x + 16) + (x + 9) + (7x + 2) = 180
Now, let's solve the equation for x:
Combine like terms: x + x + 7x + 16 + 9 + 2 = 180
Combine like terms: 9x + 27 = 180
Subtract 27 from both sides: 9x = 153
Divide both sides by 9: x = 17
Now that we have found the value of x, we can substitute it back into the expression for m∠G:
m∠G = x + 16 = 17 + 16 = 33
Therefore, the measure of angle G (m∠G) is 33 degrees.