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Angle A is larger than angle C and smaller than angle B by the same amount. In ΔABC If angle B = 67º, angle C is _____
- a)64º
- b)47º
- c)70º
- d)53º
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Angle A is larger than angle C and smaller than angle B by the same am...
Given information:
- Angle A is larger than angle C and smaller than angle B by the same amount.
- Angle B = 67
To find: Angle C
Solution:
Let x be the amount by which angle A is larger than angle C and smaller than angle B.
Then, we can write the following equations based on the given information:
- A = C + x (Angle A is larger than angle C by x)
- A = B - x (Angle A is smaller than angle B by x)
- B = 67 (Given)
Substituting B = 67 in the second equation, we get:
A = 67 - x
Substituting this value of A in the first equation, we get:
67 - x = C + x
Simplifying this equation, we get:
2x = 67 - C
Dividing both sides by 2, we get:
x = (67 - C) / 2
Substituting this value of x in the first equation (A = C + x), we get:
A = C + (67 - C) / 2
Simplifying this equation, we get:
A = (C + 67) / 2
Since the sum of angles in a triangle is 180 degrees, we have:
A + B + C = 180
Substituting the values of A and B from the above equations, we get:
(C + 67) / 2 + 67 + C = 180
Simplifying this equation, we get:
3C = 113
Dividing both sides by 3, we get:
C = 37.67
Rounding off to the nearest whole number, we get:
C = 38
Therefore, angle C is 38 degrees.
- Angle A is larger than angle C and smaller than angle B by the same amount.
- Angle B = 67
To find: Angle C
Solution:
Let x be the amount by which angle A is larger than angle C and smaller than angle B.
Then, we can write the following equations based on the given information:
- A = C + x (Angle A is larger than angle C by x)
- A = B - x (Angle A is smaller than angle B by x)
- B = 67 (Given)
Substituting B = 67 in the second equation, we get:
A = 67 - x
Substituting this value of A in the first equation, we get:
67 - x = C + x
Simplifying this equation, we get:
2x = 67 - C
Dividing both sides by 2, we get:
x = (67 - C) / 2
Substituting this value of x in the first equation (A = C + x), we get:
A = C + (67 - C) / 2
Simplifying this equation, we get:
A = (C + 67) / 2
Since the sum of angles in a triangle is 180 degrees, we have:
A + B + C = 180
Substituting the values of A and B from the above equations, we get:
(C + 67) / 2 + 67 + C = 180
Simplifying this equation, we get:
3C = 113
Dividing both sides by 3, we get:
C = 37.67
Rounding off to the nearest whole number, we get:
C = 38
Therefore, angle C is 38 degrees.
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Community Answer
Angle A is larger than angle C and smaller than angle B by the same am...
As Angle A+ B +C= 180 ,
angle angle A= angle C + z , where z is constant assume as angle A is greater than angle C by unknown value that consider z.
And angle A= angle B- z and z is constant assume as angle A is less than B by same unknown value that consider z.
so, ( A = C + z )+ (A= B - z) so,B+C=2A put it in A+ B +C = 180 , angle A+2A = 180 as B+ C= 2A, I.E. 3A=180, angle A= 60 so, 60+ 67+ angle C= 180 As B=67 :. angle C= 180-127 i.e. angle C= 53 Hence option D is accurate....
angle angle A= angle C + z , where z is constant assume as angle A is greater than angle C by unknown value that consider z.
And angle A= angle B- z and z is constant assume as angle A is less than B by same unknown value that consider z.
so, ( A = C + z )+ (A= B - z) so,B+C=2A put it in A+ B +C = 180 , angle A+2A = 180 as B+ C= 2A, I.E. 3A=180, angle A= 60 so, 60+ 67+ angle C= 180 As B=67 :. angle C= 180-127 i.e. angle C= 53 Hence option D is accurate....
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Angle A is larger than angle C and smaller than angle B by the same amount. In ΔABC If angle B = 67º, angle C is _____a)64ºb)47ºc)70ºd)53ºCorrect answer is option 'D'. Can you explain this answer?
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