Question

If PQRS is a rhombus, find the measure of angle PQR.

Answer 1

Answer:

As, we know that the diagonals of a rhombus

bisect each other equally.

so, 4x -27=2x +7

4x-2x=7+27

2x=34

x=17

angle PQR=4*17-27+2*17+7(4x-27+2x+7)

68-27+34+7

41+41=82degree

Answer 2

Answer:

82°

Rhombus:

A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is sometimes referred to as a diamond or rhombus. Rhombi or rhombuses are the plural forms of rhombus.

Both a square and a rhombus have equal numbers of sides. The square's diagonals are also perpendicular to one another and divide the opposing angles. A square is a rhombus as a result.

Step-by-step explanation:

$4x-27=2x+7$

Subtract 2x from both sides

$2x-27=7$

Add 27 to both sides

$2x=34$

Divide 2 from both sides

$x=17$

plug it in

$\angle PQS= 4(17)-27=41$

$\angle SQR= 2(17)+7=41$

Add them

$\angle PQS+\angle SQR= m\angle PQR$

$41+41= 82\textdegree$

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