Question

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

Explanation:

Step1: Set angles equal (rhombus bisector)

$2x + 13 = 3x - 12$

Step2: Solve for x

$13 + 12 = 3x - 2x$
$x = 25$

Step3: Calculate one angle measure

$m\angle SPR = 2(25) + 13 = 63^\circ$

Step4: Find total angle $\angle SPQ$

$m\angle SPQ = 2 \times 63 = 126^\circ$

Answer:

$126$