Question

What is the measure of ∠SPQ in this rhombus?

m∠SPR=(4x+11)°

m∠QPR=(5x−4)°

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Answer 1

Answer:

m∠SPQ=$142\°$

Step-by-step explanation:

we know that

In a Rhombus the diagonals bisect the angles,

so

m∠SPR=m∠QPR

substitute the values

$(4x+11)\°=(5x-4)\°$

solve for x

$5x-4x=11+4$

$x=15\°$

m∠SPQ=m∠SPR+m∠QPR

m∠SPQ=$(4x+11)\°+(5x-4)\°$

m∠SPQ=$(9x+7)\°$

m∠SPQ=$(9*15+7)\°=142\°$