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:
D
Step-by-step explanation:
Given
6x² - 2x + 36 = 5x² + 10x ( subtract 5x² + 10x from both sides )
x² - 12x + 36 = 0 ← in standard form
(x - 6)² = 0 ← in factored form, thus
x - 6 = 0 ⇒ x = 6 → D
Step-by-step explanation:
This means that if a line is perpendicular to a line that has slope m, then the slope of the line is -1 / m. For example, we found that the slope of the line y = (1/2)x + 3 is 1/2. Thus any line that is perpendicular to this line would have slope -2 /1 = -2.
