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:
Company a= 15x+10y+25z+75
Company b=20x+10y+30z+60
Step-by-step explanation:
The complete question is as follows.
The equation a = 
can be used to determine the area , <em>a</em>, of a trapezoid with height , h, and base lengths, 
and 
. Which are equivalent equations?
(a) 
(b) 
(c) 
=
(d) 
(e) 
= h
Answer: (a) ; (d) ;
Step-by-step explanation: To determine :
a =
2a = (
)h
To determine h:
a =
2a = 
= h
To determine
a =
2a =
Checking the alternatives, you have that and = h, so alternatives <u>A</u> and <u>D</u> are correct.
Answer:
Marta need to score at least 94 to receive an average of 90 or higher considering all five tests.
Explanation:
Marks received by Marta in four tests = 86, 84, 97 and 89
Let mark received in fifth test be x
We have average of five test is more than or equal to 90
So we have
So Marta need to score at least 94 to receive an average of 90 or higher considering all five tests.
Answer:
B or A.
Step-by-step explanation:
