the amount of gasoline at a gas station changes from 58,432.4 gallon to 56,475.2 gallon from 2:00 pm to 4:00 pm. what rational n
1 answer:
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Answer:
Three-fourths
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
∠QSR≅∠XZY ---> given problem
∠QRS≅∠XYZ ---> given problem
so
△QRS ~ △XYZ ----> by AA Similarity theorem
Remember that, if two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
That means
∠Q≅∠X
∠R≅∠Y
∠S≅∠Z
<em>In the right triangle XYZ</em>
Find the tangent of angle X
---> opposite side angle X divided by adjacent side angle X
substitute the given values
Simplify
Remember that
∠Q≅∠X
so
therefore
---->Three-fourths
Answer:
34°
Step-by-step explanation:
If m∠ADE is with 34° smaller than m∠CAB, then denote
m∠ADE=x°,
m∠CAB=(x+34)°.
Since DE ║ AB, then
m∠ADE=m∠DAB=x°.
AD is angle A bisector, then
m∠EAD=m∠DAB=x°.
Thus,
m∠CAB=m∠CAD+m∠DAB=(x+x)°=2x°.
On the other hand,
m∠CAB=(x+34)°,
then
2x°=(x+34)°,
m∠ADE=x°=34°.
