Answer:
103
Step-by-step explanation:
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:
The answers to each part are:
Part A.
- <u>The quantity of apples is one-third of the quantity of grapes</u>.
Part B.
- <u>The quantity of apples is a quarter of the quantity of strawberries</u>.
Part C.
- <u>The number of cherries is two-elevenths of the total fruit</u>.
Step-by-step explanation:
To identify the answer in each case, you must remember that all the parts are equal, then:
Part A.
The parts of apples are 1 and the parts grapes are 3, so if you divide the first quantity with the second quantity you obtain:
So, <u>the quantity of apples is one-third of the quantity of grapes</u> or the quantity of apples is three times smaller than the quantity of grapes.
Part B.
The parts of apples are 1 and the parts of strawberries are 4, then you must divide the first quantity with the second quantity:
In this case, <u>the quantity of apples is a quarter of the quantity of strawberries</u> or the quantity of apples is four times smaller than the quantity of strawberries.
Part C.
First, you must add all the part of fruit:
- <em>1 part apple</em>
- <em>1 part orange</em>
- <em>4 parts strawberry</em>
- <em>2 parts cherry </em>
- <em>3 parts grape</em>
The total of fruits is 11 parts, taking into account the quantity of cherries is 2, now you can divide the number of cherries with the total parts of fruit:
- 2 / 11 = 2/11 (two-elevenths)
Now, you can see <u>the number of cherries is two-elevenths of the total fruit</u>.
Answer:
what?
Step-by-step explanation:
Answer:
x = 2 sqrt(3)/3
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 60 = 1 /x
x sin 60 =1
x = 1 /sin 60
x = 1 / sqrt(3)/2
x = 2 sqrt(3)/3
