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In an obtuse triangle, the difference between the obtuse angle and one of the acute angles of a triangle is 20°, while the difference between the two acute angles is 56°. Find the measure (in degrees) of the smallest angle of the triangle.
- a)15
- b)16
- c)12
- d)10
Correct answer is option 'B'. Can you explain this answer?
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In an obtuse triangle, the difference between the obtuse angle and on...
Let the obtuse angle be a, and the acute angles be b and c.
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Now, given that
a - b = 20 => a = 20 + h and
b - c = 56 => c = b - 56
Also, a + b + c = 180 => (20 + b) + b + (b - 56) = 180
=> 3b = 216 or b = 72 => a = 20 + 72 = 92
and c = 72 - 56 = 16
Most Upvoted Answer
In an obtuse triangle, the difference between the obtuse angle and on...
Given:
- The difference between the obtuse angle and one of the acute angles is 20°.
- The difference between the two acute angles is 56°.
To find:
The measure of the smallest angle of the triangle.
Let's assume the three angles of the triangle as A, B, and C, where A is the obtuse angle and B and C are the acute angles.
1. Using the given information:
A - B = 20° (Equation 1)
B - C = 56° (Equation 2)
2. Since the sum of all angles in a triangle is 180°, we can write:
A + B + C = 180° (Equation 3)
3. Let's solve the equations to find the values of A, B, and C:
From Equation 1, we have:
A = B + 20°
Substituting this value of A in Equation 3, we get:
(B + 20°) + B + C = 180°
2B + C = 160° (Equation 4)
4. Now, let's solve Equation 2 in terms of C:
B - C = 56°
C = B - 56°
Substituting this value of C in Equation 4, we get:
2B + (B - 56°) = 160°
3B - 56° = 160°
3B = 160° + 56°
3B = 216°
B = 72°
5. Substituting the value of B in Equation 2, we can find the value of C:
B - C = 56°
72° - C = 56°
C = 72° - 56°
C = 16°
6. Substituting the values of B and C in Equation 3, we can find the value of A:
A + B + C = 180°
A + 72° + 16° = 180°
A = 180° - 72° - 16°
A = 92°
7. Now, we have the values of all three angles:
A = 92°
B = 72°
C = 16°
8. The smallest angle of the triangle is 16°.
Hence, the correct answer is option (B) 16.
- The difference between the obtuse angle and one of the acute angles is 20°.
- The difference between the two acute angles is 56°.
To find:
The measure of the smallest angle of the triangle.
Let's assume the three angles of the triangle as A, B, and C, where A is the obtuse angle and B and C are the acute angles.
1. Using the given information:
A - B = 20° (Equation 1)
B - C = 56° (Equation 2)
2. Since the sum of all angles in a triangle is 180°, we can write:
A + B + C = 180° (Equation 3)
3. Let's solve the equations to find the values of A, B, and C:
From Equation 1, we have:
A = B + 20°
Substituting this value of A in Equation 3, we get:
(B + 20°) + B + C = 180°
2B + C = 160° (Equation 4)
4. Now, let's solve Equation 2 in terms of C:
B - C = 56°
C = B - 56°
Substituting this value of C in Equation 4, we get:
2B + (B - 56°) = 160°
3B - 56° = 160°
3B = 160° + 56°
3B = 216°
B = 72°
5. Substituting the value of B in Equation 2, we can find the value of C:
B - C = 56°
72° - C = 56°
C = 72° - 56°
C = 16°
6. Substituting the values of B and C in Equation 3, we can find the value of A:
A + B + C = 180°
A + 72° + 16° = 180°
A = 180° - 72° - 16°
A = 92°
7. Now, we have the values of all three angles:
A = 92°
B = 72°
C = 16°
8. The smallest angle of the triangle is 16°.
Hence, the correct answer is option (B) 16.
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In an obtuse triangle, the difference between the obtuse angle and one of the acute angles of a triangle is 20°, while the difference between the two acute angles is 56°. Find the measure (in degrees) of the smallest angle of the triangle.a) 15b) 16c) 12d) 10Correct answer is option 'B'. Can you explain this answer?
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