Question

Pls help! Homework for Geometry 10th grade.

Answer 1

Part 22)
`m\angle 3=45^o`

Part 23)
`XQ=15\ units`

Part 24)
`m\angle 5=90^o`

Part 25)
`m\angle 1=20^o`

Part 26)
`GI=20\ units`

Part 27)
`JM=10\ units`

Explanation:

Part 22) Find the measure of angle 3

we know that

The diagonals of a square are perpendicular bisectors of each other, and diagonals bisect the angles

so

`m\angle 3+m\angle 4=90^o` --> The measure of each interior angle of a square is 90 degrees

`m\angle 3=m\angle 4` ---> diagonals bisect the angles

therefore

`m\angle 3=45^o`

Part 23) Find the length of segment XQ

we know that

`XQ=(1)/(2)ZX` ---> diagonals of a square are perpendicular bisectors of each other

we have

`ZX=30\ units`

substitute

`XQ=(1)/(2)(30)=15\ units`

Part 24) Find the measure of angle 5

we know that

`m\angle Q+m\angle 5=180^o` -->form a linear pair

Remember that

Diagonals of a square are perpendicular bisectors of each other

so

tex]m\angle Q=m\angle 5[/tex]

therefore

`m\angle 5=90^o`

Part 25) Find the measure of angle 1

we know that

The measure of each interior angle of a rectangle is 90 degrees

so

`m\angle 1+m\angle 2=90^o` ---> by complementary angles

we have that

`m\angle 2=70^o`

substitute

`m\angle 1+70^o=90^o`

`m\angle 1=90^o-70^o`

`m\angle 1=20^o`

Part 26) Find the measure of GI

we know that

The diagonals of a rectangle are congruent

so

JH=GI

we have

`JH=20\ units`

therefore

`GI=20\ units`

Part 27) Find the measure of JM

we know that

In a rectangle, the point where the diagonals intersect, divides each diagonal into two equal parts

so

`JM=MH`

`JM=(1)/(2)JH`

we have

`JH=20\ units`

substitute

`JM=(1)/(2)(20)`

`JM=10\ units`