Question

what is the measure of $\angle spq$ in this rhombus?
$m\angle spr = (2x + 13)^\circ$
$m\angle qpr = (3x - 12)^\circ$
enter your answer in the box.
$m\angle spq = \square^\circ$

Explanation:

Step1: Recall rhombus angle property

In a rhombus, the diagonal bisects the angles. So, \( \angle SPR=\angle QPR \).
Set \( 2x + 13=3x - 12 \).

Step2: Solve for x

Subtract \( 2x \) from both sides: \( 13=x - 12 \).
Add 12 to both sides: \( x = 25 \).

Step3: Find \( m\angle SPR \) and \( m\angle QPR \)

Substitute \( x = 25 \) into \( 2x+13 \): \( 2(25)+13=50 + 13=63^\circ \).
So, \( m\angle SPR=m\angle QPR = 63^\circ \).

Step4: Calculate \( m\angle SPQ \)

\( \angle SPQ=\angle SPR+\angle QPR \), so \( m\angle SPQ=63 + 63=126^\circ \).

Answer:

\( 126 \)