In triangle EFG, M<F=3(m<G), and m<E=m<F-30degree. Find the measure of each angle.
To find the measure of each angle in triangle EFG, let's start by assigning variables to the angles:
Let E be angle EFG
Let F be angle FEG
Let G be angle EGF
We are given the following information:
1. M<F = 3(m<G)
This tells us that angle M is less than angle F, and angle F is three times angle G.
So we can write: M < F and F = 3G.
2. m<E = m<F - 30°
This tells us that angle E is 30 degrees less than angle F.
So we can write: E = F - 30°.
Now let's solve for the angles:
From the information in equation 1, we have: F = 3G.
Substituting this into equation 2, we get: E = 3G - 30°.
Since the sum of the angles in a triangle is always 180 degrees, we can write the equation: E + F + G = 180°.
Substituting the values of E and F from the equations above, we get: (3G - 30°) + (3G) + G = 180°.
Simplifying the equation, we have: 7G - 30° = 180°.
Adding 30° to both sides of the equation, we get: 7G = 210°.
Dividing both sides of the equation by 7, we find: G = 30°.
Substituting this value back into equation 1, we find: F = 3G = 3(30°) = 90°.
Finally, substituting the values of F and G into equation 2, we find: E = F - 30° = 90° - 30° = 60°.
Therefore, the measure of angle E is 60°, the measure of angle F is 90°, and the measure of angle G is 30°.