Question

for exercises 7-12, find the value of x for each figure. 7. 38° 8. 94° 39° 9. 43° 81° 10. 19° 81° 11. 41° 115° 12. 41° 36°

Explanation:

Step1: Recall exterior - angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.

Step2: Solve for Exercise 7

In the triangle of Exercise 7, the two non - adjacent interior angles to the exterior angle \(x\) are \(38^{\circ}\) and \(70^{\circ}\). So \(x=38 + 70\).
\(x = 108^{\circ}\)

Step3: Solve for Exercise 8

For the triangle in Exercise 8, the non - adjacent interior angles to the exterior angle \(x\) are \(39^{\circ}\) and \(94^{\circ}\). Then \(x=39 + 94\).
\(x = 133^{\circ}\)

Step4: Solve for Exercise 9

In the triangle of Exercise 9, the non - adjacent interior angles to the exterior angle \(x\) are \(43^{\circ}\) and \(81^{\circ}\). So \(x=43+81\).
\(x = 124^{\circ}\)

Step5: Solve for Exercise 10

For the triangle in Exercise 10, the non - adjacent interior angles to the exterior angle \(x\) are \(19^{\circ}\) and \(81^{\circ}\). Then \(x=19 + 81\).
\(x = 100^{\circ}\)

Step6: Solve for Exercise 11

In the triangle of Exercise 11, the non - adjacent interior angles to the exterior angle \(x\) are \(41^{\circ}\) and \(115 - 41=74^{\circ}\) (first find the third interior angle of the triangle as \(180-(115 + 41)=24^{\circ}\), and then use the exterior - angle property). So \(x=41+(180 - 115)\).
\(x = 106^{\circ}\)

Step7: Solve for Exercise 12

For the triangle in Exercise 12, the non - adjacent interior angles to the exterior angle \(x\) are \(41^{\circ}\) and \(36^{\circ}\). Then \(x=41 + 36\).
\(x = 77^{\circ}\)

Answer:

Exercise 7: \(x = 108^{\circ}\)
Exercise 8: \(x = 133^{\circ}\)
Exercise 9: \(x = 124^{\circ}\)
Exercise 10: \(x = 100^{\circ}\)
Exercise 11: \(x = 106^{\circ}\)
Exercise 12: \(x = 77^{\circ}\)