Answer:
Part 22) [tex]m\angle 3=45^o[/tex]
Part 23) [tex]XQ=15\ units[/tex]
Part 24) [tex]m\angle 5=90^o[/tex]
Part 25) [tex]m\angle 1=20^o[/tex]
Part 26) [tex]GI=20\ units[/tex]
Part 27) [tex]JM=10\ units[/tex]
Step-by-step 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
[tex]m\angle 3+m\angle 4=90^o[/tex] --> The measure of each interior angle of a square is 90 degrees
[tex]m\angle 3=m\angle 4[/tex] ---> diagonals bisect the angles
therefore
[tex]m\angle 3=45^o[/tex]
Part 23) Find the length of segment XQ
we know that
[tex]XQ=\frac{1}{2}ZX[/tex] ---> diagonals of a square are perpendicular bisectors of each other
we have
[tex]ZX=30\ units[/tex]
substitute
[tex]XQ=\frac{1}{2}(30)=15\ units[/tex]
Part 24) Find the measure of angle 5
we know that
[tex]m\angle Q+m\angle 5=180^o[/tex] -->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
[tex]m\angle 5=90^o[/tex]
Part 25) Find the measure of angle 1
we know that
The measure of each interior angle of a rectangle is 90 degrees
so
[tex]m\angle 1+m\angle 2=90^o[/tex] ---> by complementary angles
we have that
[tex]m\angle 2=70^o[/tex]
substitute
[tex]m\angle 1+70^o=90^o[/tex]
[tex]m\angle 1=90^o-70^o[/tex]
[tex]m\angle 1=20^o[/tex]
Part 26) Find the measure of GI
we know that
The diagonals of a rectangle are congruent
so
JH=GI
we have
[tex]JH=20\ units[/tex]
therefore
[tex]GI=20\ units[/tex]
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
[tex]JM=MH[/tex]
[tex]JM=\frac{1}{2}JH[/tex]
we have
[tex]JH=20\ units[/tex]
substitute
[tex]JM=\frac{1}{2}(20)[/tex]
[tex]JM=10\ units[/tex]
