If the measure of angle dce = 4x+15 and the measure angle ecf=6x-5, find the measure of angle dce

I found a problem with the same instructions, ∡DCE = 4x + 15 and  ∡ ECF = 6x - 5, where the two mentioned angles are complementary and you need to find the measure of ∡ DCE.

So, I can explain you this case, which is likely yours, and else you can apply the same basis adapted to  your problem.

Given that the two angles are complementary their measures add up 90°.

=> 4x + 15 + 6x - 5 = 90 from which you can solve for x:

=> 10x = 90 - 15 + 5

=> 10x = 80

=> x = 80/10 = 8

So, ∡DCE = 4(8) + 15 = 32 + 15 = 47

47°.

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