Answer:
m∠FEH = 44°
m∠EHG = 64°
Step-by-step explanation:
1) The given information are;
The angle of arc m∠FEH = 272°, the measured angle of ∠EFG = 116°
Given that m∠FEH = 272°, therefore, arc ∠HGF = 360 - 272 = 88°
Therefore, angle subtended by arc ∠HGF at the center = 88°
The angle subtended by arc ∠HGF at the circumference = m∠FEH
∴ m∠FEH = 88°/2 = 44° (Angle subtended at the center = 2×angle subtended at the circumference)
m∠FEH = 44°
2) Similarly, m∠HGF is subtended by arc m FEH, therefore, m∠HGF = (arc m FEH)/2 = 272°/2 = 136°
The sum of angles in a quadrilateral = 360°
Therefore;
m∠FEH + m∠HGF + m∠EFG + m∠EHG = 360° (The sum of angles in a quadrilateral EFGH)
m∠EHG = 360° - (m∠FEH + m∠HGF + m∠EFG) = 360 - (44 + 136 + 116) = 64°
m∠EHG = 64°.
Answer:
9000
Step-by-step explanation:
4
largest:4/7×21000 = 12000
smallest: 1/7×21000. = 3000
12,000-3000 = 9000
To solve this problem, we are going to set up a system of equations, or two equations that we can use to find out two variables. Let x represent the measure of one of the side lengths, and b represent the length of the base.
We know that the sum of the two equal legs is six more than three times the length of the length of the base, or the following equation.
2x = 6 + 3b
We also know that the perimeter, or the addition of both equal side lengths and the base equals 38, or the following equation.
2x + b = 38
To solve this system of equations, we can use substitution for 2x. (This means that because we know what 2x equals in terms of b, we can substitute this value into the other equation).
6 + 3b + b = 38
Now, we have to simplify and solve this equation.
4b + 6 = 38
4b = 32
b = 8
This means that the base measures 8 cm. Because we know this measurement, we can substitute 8 into one of our beginning equations for b to solve for x.
2x + b = 38
2x + 8 = 38
2x = 30
x = 15
Therefore, the base of the triangle is 8 cm, and the equivalent side lengths both measure 15 cm.
Answer:
131.086
Step-by-step explanation:
Answer:
41 miles
Step-by-step explanation:
The first week, which is 7 days, Adam walked 2 miles a day. So, we have the multiplication equation: 2 * 7 = 14 miles.
For the next 9 days, Adam walked 3 miles per day. So, we have the multiplication equation: 3 * 9 = 27 miles.
Now, we just add these two values together:
14 + 27 = 41 miles
Thus, the answer is 41 miles.
Hope this helps!