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°.
25 metres. Because 1/10th of a kilometre is a 100 metres. And four athletes divided by 100 metres is 25 metres.
Answer:3*78=234
Step-by-step explanation:
Answer:
Step-by-step explanation:
Statements Reasons
1). m∠QPS = m∠TPV 1). Given
2). m∠QPS = m∠1 + m∠3 2). Angle addition postulate
m∠TPV = m∠2 + m∠4
3). m∠1 + m∠3 = m∠2 + m∠4 3). Given
4). m∠1 = m∠2 4). Given
5). m∠1 + m∠3 = m∠2 + m∠4 5). Subtraction property
m∠3 = m∠4
