Question

section 4.3b homework
page 223: 9 - 11, 19 - 21
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1. whats wrong with this picture? explain.

in exercises 10 - 11, use one of your new conjectures to find the missing measures.

1. $t + p =$
2. $x =$

Explanation:

Step1: Use the exterior angle theorem

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

Step2: Analyze problem 9

For problem 9, let's assume the triangle. The exterior angle (let's call it \(E\)) and the adjacent interior angle \(b\) are supplementary (\(b + 125^{\circ}=180^{\circ}\), so \(b = 55^{\circ}\)). According to the exterior angle theorem, if the exterior angle were correct, we would have \(125^{\circ}=a + 130^{\circ}\), but \(a=125^{\circ}-130^{\circ}=- 5^{\circ}\), which is impossible since angle measures cannot be negative.

Step3: Analyze problem 10

For problem 10, by the exterior angle theorem, \(t + p\) is equal to the exterior angle. The exterior angle is \(135^{\circ}\), so \(t + p=135^{\circ}\)

Step4: Analyze problem 11

For problem 11, first find the non - adjacent interior angle. The adjacent interior angle to \(144^{\circ}\) is \(180^{\circ}-144^{\circ} = 36^{\circ}\). Since the two non - adjacent interior angles are equal (marked with the same arc), and by the exterior angle theorem \(x\) (the exterior angle) is equal to the sum of the two non - adjacent interior angles. Each non - adjacent interior angle is \(36^{\circ}\), so \(x=36^{\circ}+36^{\circ}=72^{\circ}\)

Answer:

1. The angle measures are inconsistent. Using the exterior angle theorem gives a negative angle for \(a\), which is impossible.
2. \(135^{\circ}\)
3. \(72^{\circ}\)