Write and solve an equation to find the value of x for each of the triangle
Problem 1 :
Solution :
Sum of the interior angles of the triangle = 180
2x + 7 + 63 + 30 = 180
2x + 100 = 180
Subtracting 100 on both sides.
2x = 180 - 100
2x = 80
Divide by 2 on both sides.
x = 40
Problem 2 :
Solution :
Sum of interior angles = 180
115 + x + x = 180
2x + 115 = 180
Subtract 115 on both sides.
2x = 180 - 115
2x = 65
Divide it by 2.
x = 65/2
Problem 3 :
Solution:
60 + 60 + 4x - 80 = 180
120 + 4x - 80 = 180
40 + 4x = 180
Subtract 40 on both sides
4x = 180 - 40
4x = 140
Divide by 4 on both sides.
x = 140/4
x = 35
Problem 4 :
Solution :
∠A + ∠B + ∠BCA = 180
20 + 90 + ∠BCA = 180
∠BCA = 180 - 110
∠BCA = 70
∠BCD = 55
∠ACB + ∠BCD + ∠DCE = 180
70 + 55 + ∠DCE = 180
125 + ∠DCE = 180
Subtract 125 on both sides.
∠DCE = 180 - 125
∠DCE = 55
Problem 5 :
Solution :
∠A + ∠B + ∠ACB = 180
84 + 43 + ∠ACB = 180
127 + ∠ACB = 180
∠ACB = 180 - 127
∠ACB = 53
∠ACB = ∠CDE (vertically opposite angles)
∠CDE + ∠D + ∠E = 180
53 + 97 + ∠E = 180
150 + ∠E = 180
Subtract 150.
∠E = 180 - 150
∠E = 30
Problem 6 :
Solution :
∠DCE + ∠D + ∠E = 180
∠DCE + 35 + 45 = 180
∠DCE + 80 = 180
Subtract 80.
∠DCE = 180 - 80
∠DCE = 100
In triangle ACD.
∠DCE = ∠ACB = 100 (Vertically opposite angles)
∠ACB + ∠A + ∠B = 180
100 + ∠A + 52 = 180
152 + ∠A = 180
Subtracting 152 on both sides.
∠A = 180 - 152
∠A = 38
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM