Question

I already know the answer but the worksheet doesn't give an explanation. that is the only thing I need.

Answer 1

Answer: Choice C) 112 degrees

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Step-by-step explanation:

Let,

• x = measure of angle CAP = measure of angle PAB
• y = measure of angle CBP = measure of angle PBA

These equations are valid because segment AP bisects the angle CAB, i.e. it splits it into two equal pieces. Similarly, segment BP bisects angle ABC.

Then we can say,

• x+x = 2x = measure of angle CAB
• y+y = 2y = measure of angle CBA

Let's focus on triangle CAB. The three interior angles add to 180 degrees. This is true of any triangle.

(angleCAB)+(angleCBA)+(angleACB) = 180

(2x) + (2y) + (44) = 180

2x+2y+44 = 180

2(x+y+22) = 180

x+y+22 = 180/2

x+y+22 = 90

x+y = 90-22

x+y = 68

Normally we would try to isolate one variable, but I'll stop here. We'll use this later in the next section.

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Now focus your attention on triangle PAB.

The three interior angles add to 180.

(anglePAB)+(angleABP)+(angleAPB) = 180

(x)+(y)+(z) = 180

x+y+z = 180

(x+y)+z = 180

68+z = 180 .... replace "x+y" with 68

z = 180-68

z = 112 degrees is the measure of angle APB.