Question

What is the measure of ∠SPQ in this rhombus?


m∠SPR=(2x+13)°

m∠QPR=(3x−12)°

Enter your answer in the box.

°

Answer 1

Malik. I showed u how to do this already.But anyway.

Set SPR and QPR equal
2x+13=3x-12
add it all up to get x=25
substitute in 
2(25)+13 and 3(25)-12
both equal 63
Add 63+63 to get you answer which is 126.

Answer 2

Answer-

$\boxed{\boxed{m\angle SPQ=126^{\circ}}}$

Solution-

From the properties of the diagonals of the rhombus, we know that,

1. The diagonals bisect the angles.
2. The diagonals are perpendicular bisectors of each other.

Using the property 1, we can say that

$\Rightarrow m\angle SPR= m\angle QPR$

$\Rightarrow 2x+13=3x-12$

$\Rightarrow 3x-2x=13+12$

$\Rightarrow x=25$

So,

$m\angle SPR=2x+13=2\cdot 25+13=63\\\\m\angle QPR=3x-12=3\cdot 25-12=63$

As,

$m\angle SPQ=m\angle SPR+m\angle QPR$

$=63+63\\\\=126$