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a. Draw a circle. Place points A,B, and C on it in such positions that

\[mABÁåœ+mBCÁåœ\]does not equal

b. Does your example in part (a) contradict Postulate 16?

Short Answer

Expert verified

(a)The final answer is 50°and 310°.

(b)The final answer is NO.

Step by step solution

01

a.Step 1. Given information:

The given information is about the circle where mABÁåœ and mBCÁåœ are the arcs of the circle.

02

Step 2. Concept used:

mABÁåœ means central angle of arc ABand mBCÁåœmeans central angle of arc BC. .

In the figure shown below, it is clear that mABÁåœ+mBCÁåœ does not equal to mACÁåœ.

03

Step 3. Applying the concept:

mABmeans central angle of arc ABand mBCÁåœmeans central angle of arc BC..

In the figure shown below, it is clear that mABÁåœ+mBCÁåœdoes not equal to mACÁåœ.

Here,mABÁåœ=90+110=200

mBCÁåœ=110mACÁåœ=90

04

b.Step 1. Given information:

The given information is about the circle where mABÁåœ and mBCÁåœ are the arcs of the circle

05

Step 2. Concept used:

mABÁåœmeans central angle of arc ABand mBCÁåœmeans central angle of arc BC. .

In the figure shown below, it is clear that mABÁåœ+mBCÁåœ does not equal to mACÁåœ.

06

Step 3. Applying the concept:

mABÁåœmeans central angle of arc ABand mBCÁåœmeans central angle of arc BC..

In the figure shown below, it is clear that mABÁåœ+mBCÁåœdoes not equal to mACÁåœ.

Here,mABÁåœ=90+110=200

mBCÁåœ=110mACÁåœ=90

According to theorem,

mACÁåœ+mBCÁåœ=mABÁåœ

It does not contradict the postulate, here points are interchanged.

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