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:
y = 9
Step-by-step explanation:
We notice that both points have a y-coordinate of 9. Since they are the same, the equation must be y = 9 because the function can't "dip" or "rise", otherwise it would be a piecewise function and not a linear function. The equation y = 9 basically means that no matter what x is, y will always be 9.
Makes no sense.
p.s i am a fourth grader
Answer:
Step-by-step explanation:
Answer:
Correct answer: sa · sb = 2/3 · (- 3/2) = - 1
Step-by-step explanation:
Given:
line A - (x₁, y₁) = (3, -4) and (x₂, y₂) = (6, -2)
line B - (x₁, y₁) = (-1, 5) and (x₂, y₂) = (1, 2)
The slope is calculated using the following formula:
s = (y₂ - y₁) / (x₂ - x₁)
sa = (-2 - (-4)) / (6 - 3) = (-2 + 4) / 3 = 2 / 3
sa = 2 / 3
sb = (2 - 5) / (1 - (-1)) = -3 / 2
when lines are perpendicular to each other then the slopes are in the next relationship:
sa · sb = - 1
we will check:
sa · sb = 2/3 · (- 3/2) = - 1
God is with you!!!
