Question

Find the measure of ∠D∠D. 

Answer 1

The sum of the internal angles in a quadrangle is 360°, therefore we have the equation:

$90+(8x+61)+(5x-12)+(9x+1)=360\\\\(8x+5x+9x)+(90+61-12+1)=360\\\\22x+140=360\ \ \ \ |-140\\\\22x=220\ \ \ |:22\\\\x=10$

$m\angle D=5x-12$

Substitute the value of x:

$m\angle D=5(10)-12=50-12=38$

Answer: m∠D = 38 degrees

Answer 2

Sum of all four angles of a quadrilateral is 360°. So,

∠A +∠B +∠C +∠D = 360.

8x+ 61 + 90 + 9x + 1 + 5x - 12 = 360

22x + 140 = 360 Combine the like terms.

22x + 140 - 140 = 360 - 140 Subtract 140 from each sides.

22x = 220

$\frac{22x}{22} =\frac{220}{22}$ Divide each sides by 22 to isolate x.

So, x = 10.

Next step is to plug in x = 10 in 5x - 12 to get the measure of <D.

So, ∠D = 5x - 12

= 5(10) - 12

= 50 - 12

= 38.

So, ∠D = 38°

" Hope this helps to you."