Question

Trapezoids and kites

Answer 1

QUESTION 3

The sum of the interior angles of a kite is $360\degree$.

$\Rightarrow 36\degree +70\degree+m$.

$\Rightarrow 106\degree+m$.

$\Rightarrow m$.

$\Rightarrow m$.

But the two remaining opposite angles of the kite are congruent.

$\Rightarrow m$

$\Rightarrow m$.

$\Rightarrow 2m$.

$\Rightarrow m$.

$\Rightarrow m$.

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;

$|RH|^2=12^2+20^2$

$|RH|^2=144+400$

$|RH|^2=544$

$|RH|=\sqrt{544}$

$|RH|=4\sqrt{34}$

QUESTION 5

The given figure is an isosceles trapezium.

The base angles of an isosceles trapezium are equal.

Therefore $m$

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;

$m$

$\Rightarrow m$

$\Rightarrow m$

QUESTION 7

The sum of the interior angles of a kite is $360\degree$.

$\Rightarrow 48\degree +110\degree+m$.

$\Rightarrow 158\degree+m$.

$\Rightarrow m$.

$\Rightarrow m$.

But the two remaining opposite angles are congruent.

$\Rightarrow m$

$\Rightarrow m$.

$\Rightarrow 2m$.

$\Rightarrow m$.

$\Rightarrow m$.

QUESTION 8

The diagonals of the kite meet at right angles.

The length of BC can also be found using Pythagoras Theorem;

$|BC|^2=4^2+7^2$

$\Rightarrow |BC|^2=16+49$

$\Rightarrow |BC|^2=65$

$\Rightarrow |BC|=\sqrt{65}$

QUESTION 9.

The sum of the interior angles of a trapezium is $360\degree$.

$\Rightarrow m$.

$\Rightarrow m$.

But the measure of angle M and K are congruent.

$\Rightarrow m$.

$\Rightarrow m$.

$\Rightarrow m$.

$\Rightarrow m$.