The parking spaces in a city lot were created by painting rows of parallel line segments, then painting a line that cuts through
each of the parallel segments. A sketch of two parking spaces is shown below. 2 diagonal parallel lines are cut by a horizontal transversal. Where the first parallel line intersects the transversal, the top right angle is angle 1. Where the second parallel line intersects the transversal, the top left angle is angle 2. If m∠2 = 115°, what is m∠1?
2 answers:
Answer:
65°
Step-by-step explanation:
The consecutive interior angles theorem states that if two parallel lines are cut by a transversal line then the resulting pair of consecutive angles formed are supplementary (that is they add up to 180°).
Given that the painting rows are parallel to each other and a painted line (transversal) cut the parallel lines forming consecutive interior angles m∠1 and m∠2. Therefore:
m∠1 + m∠2 = 180°
m∠1 + 115 = 180
m∠1 = 180 - 115
m∠1 = 65°
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Yo sup??
The two triangles are similar by AAA property ie
Angle Angle Angle property
Let us name the two triangles as ABC and DEF
By observing the figure
mB=mE=90 (right angled triangle)
mA=mD (parallel lines property)
mC=mF (parallel lines property)
Therefore by AAA the two triangles are similar .
The diagram is given below.
PS: All the credits for image goes to Picasso-PSN03
Step-by-step explanation:
hope it will helps you my answer
