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zlopas [31]
3 years ago
15

Trapezoids and kites

Mathematics
1 answer:
lisov135 [29]3 years ago
6 0

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.

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