Question

solve for x.
11)
a) 3 b) 9
c) 6 d) 15
13)
a) 4 b) 12
c) 14 d) 6
12)
a) 10 b) 5
c) 14 d) 8
14)
a) 5 b) 8
c) 15 d) 14

Explanation:

Step1: Use exterior - angle property of a triangle

For problem 11: The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(70=(9x + 3)+(13x+1)\).
Combine like terms: \(70 = 22x+4\).

Step2: Solve the resulting equation for \(x\)

Subtract 4 from both sides: \(70 - 4=22x\), so \(66 = 22x\).
Divide both sides by 22: \(x=\frac{66}{22}=3\).

Step3: For problem 12

Using the exterior - angle property of a triangle, \(54=(3x + 9)+6x\).
Combine like terms: \(54 = 9x+9\).

Step4: Solve the equation for \(x\)

Subtract 9 from both sides: \(54 - 9=9x\), so \(45 = 9x\).
Divide both sides by 9: \(x = 5\).

Step5: For problem 13

Using the exterior - angle property of a triangle, \(124=(15x - 1)+(4x + 11)\).
Combine like terms: \(124=19x + 10\).

Step6: Solve the equation for \(x\)

Subtract 10 from both sides: \(124-10 = 19x\), so \(114=19x\).
Divide both sides by 19: \(x=\frac{114}{19}=6\).

Step7: For problem 14

Using the exterior - angle property of a triangle, \(11x + 7=(2x + 14)+65\).
Combine like terms: \(11x+7=2x + 79\).

Step8: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(11x-2x+7=79\), so \(9x+7 = 79\).
Subtract 7 from both sides: \(9x=79 - 7=72\).
Divide both sides by 9: \(x = 8\).

Answer:

1. A. 3
2. B. 5
3. D. 6
4. B. 8