Find the value of b.

Mathematics

1 answer:

Nesterboy [21]2 years ago

7 0

Answer: $230^{\circ$

Step-by-step explanation:

For convenience, I labeled some points as shown in the attached picture.

Also, I assume $\overline{AB}$ and $\overline{BC}$ are tangents to the circle.

$\overline{BO} \cong \overline{BO}$ (reflexive property)
$\overline{AB} \cong \overline{BC}$ (tangents drawn from a common external point are congruent)
$\angle BAO \cong \angle BCO$ (right angles are congruent)

Therefore, we know $\triangle ABO \cong \triangle CBO$ by HL.

Thus, by CPCTC,

$\angle AOB \cong \angle BOC \implies m\angle BOC=65^{\circ}\\\\\implies m\angle AOC=130^{\circ}$

This means the measure of minor arc AC is $130^{\circ}$ , and thus $b=360^{\circ}-130^{\circ}=\boxed{230^{\circ}}$

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Here are two polygons on a grid. Is PQRST a scaled copy of ABCDE?

Bezzdna [24]

*see attachment showing the two polygons in a grid.

Answer:

No, PQRST is not a scale copy of ABCDE because we the sides are not increased proportionally.

Step-by-step explanation:

A polygon can be said to be a scaled copy of another polygon, if the the same scale factor is used in scaling every segment of the preimage or original image to get the length of the corresponding segments of the scale copy or image. In order words, all segments must be scaled proportionally.

Polygon PQRST, which is the new image, has different scale factors used in scaling the various segments of the preimage. In simple terms, the sides of PQRST were not increased proportionally. Therefore, PQRST is not a scaled copy of ABCDE.