Question

there is a parallelogram (judging from the marks of equal sides and parallel sides) with angle a labeled as ((15c - 10)^circ), angle i (maybe angle c? or a typo, assuming its related to the parallelogram angles) labeled as ((10c + 20)^circ), angle d labeled as ((2d - 100)^circ), and angle b labeled as (d^circ). then there are questions: ( angle a = ), ( angle i = ) (maybe ( angle c )), ( c = ), ( angle b = ), ( angle d = ), ( d = )

Explanation:

Step1: Set equal opposite angles

$15c - 10 = 10c + 20$

Step2: Solve for c

$15c - 10c = 20 + 10$
$5c = 30$
$c = \frac{30}{5} = 6$

Step3: Calculate $\angle A$ and $\angle I$

$\angle A = 15(6) - 10 = 90 - 10 = 80^\circ$
$\angle I = 10(6) + 20 = 60 + 20 = 80^\circ$

Step4: Set supplementary adjacent angles

$d + 80 = 180$

Step5: Solve for d

$d = 180 - 80 = 100$

Step6: Calculate $\angle D$

$\angle D = 2(100) - 100 = 200 - 100 = 100^\circ$
$\angle B = d = 100^\circ$

Answer:

$d = 100$
$\angle D = 100^\circ$
$\angle B = 100^\circ$
$c = 6$
$\angle I = 80^\circ$
$\angle A = 80^\circ$