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Lina20 [59]
3 years ago
14

Someone help me solve 10-16 please thank you!

Mathematics
1 answer:
SVEN [57.7K]3 years ago
7 0

Answer:

Part 10)

a) OM=46\ units

b) PN=23\ units

c) ON=23\sqrt{2}\ units

d) MN=23\sqrt{2}\ units

Part 12) x=11

Part 14) see the explanation

Step-by-step explanation:

Part 10) we know that

In a square all four sides are congruent

The diagonals of a square are congruent and bisect each other at right angles

Part a)

Find the length of diagonal OM

we know that

OM=LN ---> the diagonals are congruent

we have

LN=46\ units

therefore

OM=46\ units

Part b)

Find the length of PN

we know that

PN=PL ---> remember that the diagonals bisect each other

PN=\frac{LN}{2}

we have

LN=46\ units

substitute

PN=\frac{46}{2}=23\ units

Part c)

Find the length of ON

Applying the Pythagorean Theorem

OM^2=ON^2+MN^2

we know that

ON=MN ----> remember that all four sides are congruent

so

OM^2=2ON^2

OM=46\ units

substitute

46^2=2ON^2

2,116=2ON^2

1,058=ON^2

ON=\sqrt{1,058}\ units

simplify

ON=23\sqrt{2}\ units

Part d)

Find the length of MN

we know that

MN=ON ----> remember that all four sides are congruent

we have

ON=23\sqrt{2}\ units

therefore

MN=23\sqrt{2}\ units

Part 12) we know that

The diagonals of a square bisect its angles

Remember that the interior angles of a square is 90 degrees

so

(6x-21)\°=45\°

solve for x

6x=45+21\\6x=66\\x=11

Part 14) we know that

A parallelogram has opposite parallel sides, so a parallelogram will always have consecutive supplementary angles.

The rectangle, rhombus and a square are all parallelograms

therefore

parallelograms, rectangles,rhombi and squares will always have consecutive supplementary angles.

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