Question

PQRS is a rhombus, with diagonal PR¯¯¯¯¯¯¯¯

and the following measurements:



m∠SPR=(3x + 12)∘

m∠QPR=(4x−6)∘



What is the measure of ∠SPQ
in this rhombus?

Answer 1

132

Explanation:

Answer 2

`m\angle SPQ=132^o`

Explanation:

step 1

Find the value of x

we know that

In a Rhombus the diagonals bisect the angles

so

`m\angle SPR=m\angle QPR`

substitute the given values

`3x+12=4x-6`

solve for x

`4x-3x=12+6`

`x=18`

step 2

Find the measure of ∠SPQ

we know that

`m\angle SPQ=m\angle SPR+m\angle QPR` ---> by addition angles postulate

`m\angle SPR=(3(18)+12)=66^o`

`m\angle QPR=(4(18)-6)=66^o`

substitute

`m\angle SPQ=66^o+66^o=132^o`