Question

Unit 7: Polygons and Quadrilaterals Homework 6: Kites Need Help Stat PLEASE HELP!!!!! 20 POINTS

Answer 1

1) The measures of angles H and F are 121°, respectively.

2) The measures of angles U and V are 65° and 139°, respectively.

3) The missing angles are $m \angle 1 = 72^{\circ}$, $m\angle 2 = 72^{\circ}$, $m\angle 3 = 47^{\circ}$, $m\angle 4 = 90^{\circ}$, $m\angle 5 = 18^{\circ}$, $m\angle 6 = 47^{\circ}$ and $m\angle 7 = 43^{\circ}$.

4) The missing angles are $m \angle 1 = 55^{\circ}$, $m\angle 2 = 35^{\circ}$, $m\angle 3 = 35^{\circ}$, $m\angle 4 = 90^{\circ}$, $m \angle 5 = 55^{\circ}$, $m \angle 6 = 67^{\circ}$, $m\angle 7 = 67^{\circ}$, $m\angle 8 = 23^{\circ}$ and $m \angle 9 = 23^{\circ}$, respectively.

5) The measure of side $QT$ is $\sqrt{105}$.

6) The measure of side $DF$ is $4\sqrt{26}$.

7) The measure of side $NP$ is $3\sqrt{65}$.

8) The value of $x$ is 17.

9) The value of $x$ is 6.

10) The measure of angle EDC is 107°.

11) The measure of angle RST is 122°.

How find missing angles and sides in rhombuses

1) According to geometry, the sum of internal angles in a quadrilateral equals 360°. Since the given figure is a kite-type rhombus, the measures of angles H and F are 121°, respectively. $\blacksquare$

2) According to geometry, the sum of internal angles in a quadrilateral equals 360°. Since the given figure is a kite-type rhombus, the measures of angles U and V are 65° and 139°, respectively. $\blacksquare$

3) According to geometry, the sum of internal angles in a triangle equals 180° and the sum of internal angles in a quadrilateral equals 360°. The missing angles are $m \angle 1 = 72^{\circ}$, $m\angle 2 = 72^{\circ}$, $m\angle 3 = 47^{\circ}$, $m\angle 4 = 90^{\circ}$, $m\angle 5 = 18^{\circ}$, $m\angle 6 = 47^{\circ}$ and $m\angle 7 = 43^{\circ}$, respectively. $\blacksquare$

4) According to geometry, the sum of internal angles in a triangle equals 180° and the sum of internal angles in a quadrilateral equals 360°. The missing angles are $m \angle 1 = 55^{\circ}$, $m\angle 2 = 35^{\circ}$, $m\angle 3 = 35^{\circ}$, $m\angle 4 = 90^{\circ}$, $m \angle 5 = 55^{\circ}$, $m \angle 6 = 67^{\circ}$, $m\angle 7 = 67^{\circ}$, $m\angle 8 = 23^{\circ}$ and $m \angle 9 = 23^{\circ}$, respectively. $\blacksquare$

5) In this case we need to apply Pythagorean theorem and triangle and quadrilateral properties to determine the missing side:

$QT = \sqrt{PQ^{2}-PT^{2}}$

$QT = \sqrt{13^{2}-8^{2}}$

$QT = \sqrt{105}$

The measure of side $QT$ is $\sqrt{105}$. $\blacksquare$

6) In this case we need to apply Pythagorean theorem and triangle and quadrilateral properties to determine the missing side:

$DF = 2\cdot DH$, $DH = \sqrt{DE^{2}-EH^{2}}$

$DF = 2\cdot \sqrt{DE^{2}-EH^{2}}$

$DF = 2\sqrt{15^{2}-11^{2}}$

$DF = 4\sqrt{26}$

The measure of side $DF$ is $4\sqrt{26}$. $\blacksquare$

7) In this case we need to apply Pythagorean theorem and triangle and quadrilateral properties to determine the missing side:

$NK = 7\cdot x - 1$, $NM = 10\cdot x - 13$, $KM = 24$, $NK = NM$, $KP = \frac{KM}{2}$

$NP = \sqrt{NK^{2}-KP^{2}}$

$NP = \sqrt{[7\cdot (4)-1]^{2}-12^{2}}$

$NP = 3\sqrt{65}$

The measure of side $NP$ is $3\sqrt{65}$. $\blacksquare$

8) According to geometry, the sum of internal angles in a quadrilateral equals 360°. Since the given figure is a kite-type rhombus, the value of $x$ is 17. $\blacksquare$

9) According to geometry, the sum of internal angles in a quadrilateral equals 360°. Since the given figure is a kite-type rhombus, the value of $x$ is 6. $\blacksquare$

10) According to geometry, the sum of internal angles in a triangle equals 180°. Hence, we have the following expressions:

$m\angle EDC = 180^{\circ}-90^{\circ}-[2\cdot (2)+13]$

$m\angle EDC = 107^{\circ}$

The measure of angle EDC is 107°. $\blacksquare$

11) According to geometry, the sum of internal angles in a triangle equals 180°. Hence, the angle RST is:

$m\angle RST = 2\cdot (3\cdot 12 +25)$

$m \angle RST = 122^{\circ}$

The measure of angle RST is 122°. $\blacksquare$

To learn more on quadrilaterals, we kindly invite to check this verified question: https://brainly.com/question/25240753