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KonstantinChe [14]
3 years ago
13

PR and PS are tangent to center Q. Find the measurement of angle Q.

Mathematics
2 answers:
Mars2501 [29]3 years ago
8 0
Angle Q is supplementary to angle P (42°), so is 138°.
Veronika [31]3 years ago
5 0

Given, in the figure PR and PS are two tangents. They meet at P. Here angle P given. ∠P = 42°.

If we take a straight line PQ, it will create two triangles.

We can see here angle R and angle S both are right angles.

As here two triangles, so sum of all the angles of the triangles is 180^o + 180^o = 360^o

Now if we subtract the two right angles we will get,

360^o-90^o-90^o = 360^o-180^o = 180^o

That means ∠P+∠Q = 180°

If we substitute the value of angle P we will get,

42^o+Q = 180^o

We can get angle Q by subtracting 42 to both sides. We will get,

42^o+Q-42^o = 180^o-42^o

Q = 180^o-42^o

Q = 138^o

So we have got angle Q, the measurement of ∠Q = 138°.

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Answer:

Step-by-step explanation:

Given that divisor is 24 and dividend is 1344 and we are to use box method.

Long division is often considered one of the most challenging topics to teach. Luckily, there are strategies that we can teach to make multi-digit division easier to understand and perform.

The Box Method, or  the Area Model, is one of these strategies. It is a mental math based approach that will enhance number sense understanding. Students solve the equation by subtracting multiples until they get down to 0, or as close to 0 as possible.

For example this method is shown below:

I step is to find in multiples of 10 or 100 the greatest divisor

24) 1344( 500

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Find the point, M, that divides segment AB into a ratio of 2:3 if A is at (0.15) and B is at (20.0)
timama [110]

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Notice that the points (0,15), and (20,0) form with the origin of coordinates (0,0),  a right angle triangle (please see attached image). This triangle has twon perpendicular sides of length 15 and 20 respectively. Therefore, we can find the length of the segment that joins points A (0,15) and B (20,0) by finding the length of the hypotenuse in a right angle triangle (with the Pythagorean Theorem):

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In order to find the appropriate location in (x,y) coordinates, we consider a smaller triangle (pictured in orange in the image) that is similar to the first larger triangle (pictured in blue). Notice that if the length of AB is 25,  each of its five equal divisions would be of length "5", and therefore two of them will render a length of "10" (which is the hypotenuse of this smaller right angle triangle.

Now, in order to find the sides of this smaller triangle (which can give us the clues on the horizontal and vertical coordinates of point M), we can use proportions.

To find the length "x" of the horizontal side , we do:

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To find the length "y" of the vertical side , we do:

\frac{y}{10} =\frac{15}{25} \\y=\frac{10*15}{25} \\y=6

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