Question

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

Answer 1

Answer:

$m\angle SPQ=132^o$

Step-by-step 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

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