In the diagram AB is parallel to DC.
Angle ABC = 70°
Angle ACD = 55°
Not drawn accurately
Show that triangle ABC is isosceles.
You must give reasons in your working.

Triangle ABC is an isosceles triangle.

Solution:

Given data:

∠ABC = 70° and ∠ACD = 55°

If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

m∠BAC = m∠ACD

m∠BAC = 55°

Sum of the angles in a straight line add up to 180°.

m∠ACD + m∠ACB + m∠ABC = 180°

55° + m∠ACB + 70° = 180°

m∠ACB + 125° = 180°

Subtract 125° from both sides, we get

m∠ACB = 55°

In triangle ABC,

∠BAC = 55° and ∠ACB = 55°

∠BAC = ∠ACB

Two angles in the triangle are equal.

Therefor triangle ABC is an isosceles triangle.

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation:

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles