A gym charges a membership fee plus an additional fee per yoga class. The table shows the linear relationship between the number
of yoga classes taken and the total cost including the membership fee.
Which statement is true?
Which statement is true?
1 answer:
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Answer: ∠A=48°,∠B=48°,∠C=84°.
Step by-step explanation:
Given: AD and BE are the angle bisectors of ∠A and ∠B
i.e ∠6=∠7 ( ∵ Angles formed after AD bisected ∠A)
∠4=∠5 ( ∵ Angles formed after BE bisected ∠B)
Also, DE║AB
⇒ ∠2=∠7 (∵ Alternate interior angles)
∠3=∠6 (∵ Alternate interior angles)
And ∠ADE : ∠ADB =∠2:∠3= 2:9 =2x : 9x ..(1)
To Find: ∠A,∠B,∠C.
Solution: ∠2=∠7 (∵ Given) ...(2)
∠2=∠4 (∵ angles on the same segment) ...(3)
∠4=∠5 =∠B/2 (∵ Given) ...(4)
∴ In Δ ABD
∠3+∠4+∠5+∠7 = 180 (∵ Sum of interior angles of a triangle)
From equation 2,3,4,5, Put values
9x+2x+2x+2x =180°
⇒15x = 180°
⇒x=12°
Putting values in equation (4) ⇒ ∠ B =2*(2*12) = 48°
Also, <u>∠B=∠A=48°</u>
Now,in Δ ABC
∠C+∠B+∠A= 180°
⇒48°+48°+∠C= 180°
<u><em>⇒∠C=84°</em></u>
