The measure of ∠BAF is 54°.
Solution:
DF and CE are intersecting lines.
m∠EAF = 72° and AB bisects ∠CAF.
∠EAF and ∠DAC are vertically opposite angles.
Vertical angle theorem:
<em>If two lines are intersecting, then vertically opposite angles are congruent.</em>
∠DAC ≅ ∠EAF
m∠DAC = 72°
<em>Sum of the adjacent angles in a straight line = 180°</em>
m∠DAE + m∠EAF = 180°
m∠DAE + 72° = 180°
Subtract 72° from both sides.
m∠DAE = 108°
∠CAF and ∠DAE are vertically opposite angles.
⇒ m∠CAF = m∠DAE
⇒ m∠CAF = 108°
AB bisects ∠CAF means ∠CAB = ∠BAF
m∠CAB + m∠BAF = 108°
m∠BAF + m∠BAF = 108°
2 m∠BAF = 108°
Divide by 2 on both sides, we get
m∠BAF = 54°
Hence the measure of ∠BAF is 54°.
Answer:
28 miles
Step-by-step explanation:
Let w stand for the number of miles Derrick runs each week. Then after 4 weeks of training, he wants the total mileage to be 100 miles.
16 + 3w = 100
3w = 84 . . . . . . . subtract 16
w = 28 . . . . . . . . divide by 3
Derrick will run 28 miles each week to achieve his training goal.
Answer:
x<5
Step-by-step explanation:
View Picture
Answer:
The hypotenuse is 68
Step-by-step explanation:
To find the length of the hypotenuse of a a right angled triangle, we use the Pythagoras Theorem
c² = a² + b²
where c = hypotenuse, a = height, 32 and b = width, 60
Substitute the value 32 and 60 for a and b respectively in the above formula, and we will have
c² = 32² + 60²
c² = 1024 + 3600
c² = 4624
c = √4624
c = 68
Answer:
48 boys
Step-by-step explanation:
Since the ratio of Boys to Girls is 4/3, set this equal to X number of boys/36. Cross multiply so 36*4=144, and 3*x= 3x. So now you have 144=3x, divide by 3 to get x=48 boys.
