Question

Someone help me solve 10-16 please thank you!

Answer 1

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.