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melamori03 [73]
3 years ago
7

A committee raised 7/9 of their target goal last year and another 1/9 of the goal this year. What fraction of their goal has bee

n raised
Mathematics
1 answer:
Airida [17]3 years ago
8 0

Answer:

8/9

Step-by-step explanation:

Find what fraction of their goal they have raised by adding the amounts from last year and this year together:

7/9 + 1/9

= 8/9

So, they have raised 8/9 of their goal

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In ΔABC, AD and BE are the angle bisectors of ∠A and ∠B and DE║ AB. Find the measures of the angles of ΔABC, if m∠ADE: m∠ADB = 2
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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>

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