Prove by mathematical induction that 1^2 + 2^2 ++k^2= k(k+1)(2k+1)/6

As usual, we start by checking that the base case holds: if we have

which is true. Now, we assume that

and we check : if we add the k+1-th term on both sides, we have

And our goal is to rearrange the right hand term as follows:

And we're done, because is exactly the formula if you substitute k with k+1

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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step-by-step explanation: