The variable expression represent the angle measures of a triangle. Find the measures of each angle. Then classify the triangle by its angles.
Problem 1 :
∠A = x°, ∠B = 2x°, ∠C = (2x+15)°
Solution :
Sum of angles of a triangle = 180
x + 2x + 2x + 15 = 180
5x + 15 = 180
Subtracting 15 on both sides.
5x = 180 - 15
5x = 165
Divide by 5 on both sides.
x = 165/5
x = 33
∠A = x° ∠A = 33 |
∠B = 2x° ∠B = 2(33) ∠B = 66 |
∠C = (2x+15)° ∠C = 2(33) + 15 ∠C = 66 + 15 ∠C = 81 |
Problem 2 :
∠A = x°, ∠B = 7x°, ∠C = x
Solution :
Sum of angles of a triangle = 180
x + 7x + x = 180
9x = 180
Divide by 9 on both sides.
x = 180/9
x = 20
∠A = 20, ∠B = 7(20) ==> 140, ∠C = 20
Problem 3 :
∠A = (x - 15)°, ∠B = (2x - 165)°, ∠C = 90°
Solution :
Sum of angles of a triangle = 180
x - 15 + 2x - 165 + 90 = 180
3x - 180 + 90 = 180
3x - 90 = 180
Add 90 on both sides.
3x = 180 + 90
3x = 270
Divide by 3 on both sides.
x = 270/3
x = 90
∠A = (x - 15)° ∠A = (90 - 15)° ∠A = 75° |
∠B = (2x - 165)° ∠B = (2(90) - 165)° ∠B = 180 - 165 ∠B = 15 |
Find the measure of the exterior angle shown.
Problem 4 :
Solution :
Exterior angle = 2x - 8 ---(1)
Remote interior angles are x and 31.
Sum of remote interior angle = Exterior angle
2x - 8 = x + 31
2x - x = 31 + 8
x = 39
Applying the value of x in (1), we get
= 2(39) - 8
= 78 - 8
= 70
So, the required exterior angle is 70.
Problem 5 :
Solution :
Exterior angle = 10x + 9 ------(1)
Remote interior angles are 38 and 7x + 1.
Sum of remote interior angle = Exterior angle
38 + 7x + 1 = 10x + 9
39 + 7x = 10x + 9
Subtract 7x on both sides.
39 = 10x - 7x + 9
39 = 3x + 9
Subtract 9 on both sides.
39 - 9 = 3x
3x = 30
Dividing by on both sides, we get
x = 30/3
x = 10
Applying the value of x in (1), we get
= 10(10) + 9
= 100 + 9
= 109
So, the required exterior angle is 109.
Problem 6 :
Solution :
The given triangle is right triangle.
Sum of interior angles = 180
x + 2x - 21 + 90 = 180
3x + 69 = 180
Subtracting 69 on both sides.
3x = 180 - 69
3x = 111
Dividing by 3 on both sides.
x = 111/3
x = 37
Exterior angle + x = 180
Exterior angle = 180 - x
Exterior angle = 180 - 37
Exterior angle = 143
Problem 7 :
In triangle PQR, the measure of ∠P is 36. The measure of ∠Q is five times the measure of ∠R. Find ∠Q and ∠R.
Solution :
∠P = 36,∠Q = 5∠R
∠P + ∠Q + ∠R = 180
36 + 5∠R + ∠R = 180
Subtract 36 on both sides.
6∠R = 180 - 36
6∠R = 144
Divide by 6 on both sides.
∠R = 144/6
∠R = 24
∠Q = 5(24) ==> 120
Problem 8 :
The measure of an exterior angle of a triangle is 120. The interior angles that are not adjacent to this exterior angle are congruent. Find the measures of the interior angles of the triangle.
Solution :
Let x be the required angle.
x + x = 120
2x = 120
x = 120/2
x = 60
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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