Answer:
Definition of bisector
Angle addition postulate
same side interior angles theorem
subtraction property of equality
Step-by-step explanation:
It is given that m║n, m∠1 = 65°,m∠2=60° and BD --> bisects ∠ABC . Because of triangle sum theorem, m∠3 = 55°. By the definition of bisector , ∠3 ≅∠4, so m∠4= 55°. Using the angle addition postulate , m∠ABC = 110°, m∠5 = 110° because vertical angles are congruent . Because of same side interior angles theorem, m∠5 +m∠6 = 180°. Substituting gives 110°+ m∠6 =180°, so by the subtraction property of equality , m∠6 = 70°.
Answer:
22.5 miles
Step-by-step explanation:
No traffic :
Let speed = x
Time taken = 30 = 30/60 = 0.5 hour
Speed = distance / time
Distance = d
x = d / 0.5 - - - (1)
With traffic :
Speed = x - 30
Time taken = 1 hour 30 minutes = 1.5 hour
x - 30 = d / 1.5
x = d/1.5 + 30 - - - - (2)
Equating (1) and (2)
d / 0.5 = d/1.5 + 30
d /0.5 - d /1.5 = 30
(1.5d - 0.5d) / 0.75 = 30
1.5d - 0.5d = 22.5
1d = 22.5
Hence,
d = 22.5 miles
Explanation:
Let M be the midpoint of AB. Then CM is the perpendicular bisector of AB. As such, center O is on CM, and OC is a radius (and CM). The tangent is perpendicular to that radius (and CM), so is parallel to AB, which is also perpendicular to CM.
If you need to go any further, you can show that triangles CMA and CMB are congruent, so (linear) angles CMA and CMB are congruent, hence both 90°.
Since the margin of error is 5%, the minimum of supporters will be less than the maximum of disapprovers.
So the third option will be correct. You cannot make certain conclusions based on this survey.
