QUESTION 3
The sum of the interior angles of a kite is [tex]360\degree[/tex].
[tex]\Rightarrow 36\degree +70\degree+m<\:D+m<\:B=360\degree[/tex].
[tex]\Rightarrow 106\degree+m<\:D+m<\:B=360\degree[/tex].
[tex]\Rightarrow m<\:D+m<\:B=360\degree-106\degree[/tex].
[tex]\Rightarrow m<\:D+m<\:B=254\degree[/tex].
But the two remaining opposite angles of the kite are congruent.
[tex]\Rightarrow m<\:D=m<\:B[/tex]
[tex]\Rightarrow m<\:D+m<\:D=254\degree[/tex].
[tex]\Rightarrow 2m<\:D=254\degree[/tex].
[tex]\Rightarrow m<\:D=\frac{254\degree}{2}[/tex].
[tex]\Rightarrow m<\:D=127\degree[/tex].
QUESTION 4
RH is the hypotenuse of the right triangle formed by the triangle with side lengths, RH,12, and 20.
Using the Pythagoras Theorem, we obtain;
[tex]|RH|^2=12^2+20^2[/tex]
[tex]|RH|^2=144+400[/tex]
[tex]|RH|^2=544[/tex]
[tex]|RH|=\sqrt{544}[/tex]
[tex]|RH|=4\sqrt{34}[/tex]
QUESTION 5
The given figure is an isosceles trapezium.
The base angles of an isosceles trapezium are equal.
Therefore [tex]m<\:T=60\degree[/tex]
QUESTION 6
The measure of angle Y and Z are supplementary angles.
The two angles form a pair of co-interior angles of the trapezium.
This implies that;
[tex]m<\:Y+68\degree=180\degree[/tex]
[tex]\Rightarrow m<\:Y=180\degree-68\degree[/tex]
[tex]\Rightarrow m<\:Y=112\degree[/tex]
QUESTION 7
The sum of the interior angles of a kite is [tex]360\degree[/tex].
[tex]\Rightarrow 48\degree +110\degree+m<\:Q+m<\:S=360\degree[/tex].
[tex]\Rightarrow 158\degree+m<\:Q+m<\:S=360\degree[/tex].
[tex]\Rightarrow m<\:Q+m<\:S=360\degree-158\degree[/tex].
[tex]\Rightarrow m<\:Q+m<\:S=202\degree[/tex].
But the two remaining opposite angles are congruent.
[tex]\Rightarrow m<\:Q=m<\:S[/tex]
[tex]\Rightarrow m<\:Q+m<\:Q=202\degree[/tex].
[tex]\Rightarrow 2m<\:Q=202\degree[/tex].
[tex]\Rightarrow m<\:Q=\frac{202\degree}{2}[/tex].
[tex]\Rightarrow m<\:Q=101\degree[/tex].
QUESTION 8
The diagonals of the kite meet at right angles.
The length of BC can also be found using Pythagoras Theorem;
[tex]|BC|^2=4^2+7^2[/tex]
[tex]\Rightarrow |BC|^2=16+49[/tex]
[tex]\Rightarrow |BC|^2=65[/tex]
[tex]\Rightarrow |BC|=\sqrt{65}[/tex]
QUESTION 9.
The sum of the interior angles of a trapezium is [tex]360\degree[/tex].
[tex]\Rightarrow m<\:J+m<\:K+88\degree+120\degree=360\degree[/tex].
[tex]\Rightarrow m<\:J+m<\:K+208\degree=360\degree[/tex].
But the measure of angle M and K are congruent.
[tex]\Rightarrow m<\:J+88\degree+208\degree=360\degree[/tex].
[tex]\Rightarrow m<\:J+296\degree=360\degree[/tex].
[tex]\Rightarrow m<\:J=360\degree-296\degree[/tex].
[tex]\Rightarrow m<\:J=64\degree[/tex].
