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Mathematics

1 answer:

koban [17]3 years ago

3 0

Answer:

a=42°

b=138°

Step-by-step explanation:

the sum of angles on a triangle is 180°

18+120+a=180

138+a=180

a=180-138

a=42

a+b=180 because a ans b are linear pair of angles.

Definiton:A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

a=42 from before

it means that b=180-42=138

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Rectangle ABCD is similar to rectangle RSTU .

Alenkasestr [34]

Answer:

The scale factor of a dilation from ABCD to RSTU is $\frac{1}{2}$

Step-by-step explanation:

We know that the rectangle ABCD is similar to rectangle RSTU.

Given that in rectangle ABCD the longest sides are DC and AB and in the rectangle RSTU the longest sides are UT and RS ⇒ The scale factor of a dilation will transform the sides DC and AB into UT and RS

Working with the lengths of the sides :

DC.(Scale factor) = UT

AB.(Scale factor) = RS

Replacing with the values of the lengths (Scale factor : SF) :

$DC.SF=UT\\(90ft).(SF)=45ft\\SF=\frac{45ft}{90ft} \\SF=\frac{1}{2}$