List the first 10 lucas numbers and the first ten fibonacci numbers and then prove each of the following propositions. the second principle of mathematical induction may be needed to prove some of these propositions. ? (a) for each natural number n, ln d 2fnc1 fn. (b) for each n 2 n with n 2, 5fn d ln1 c lnc1. (c) for each n 2 n with n 3, ln d fnc2

1. 180°. the sum of the interior angles of a triangle is 180°, for the equilateral triangle that it has three equals side is 60°+60°+60°=180°.

2. 60°. each interior angle of a equilateral triangle is 60°

3. 120°. the measure of ∠m is 120°, the sum of the angles ∠m and ∠n is equal to 180°. so, in order to find the measure of ∠m, we have ∠m+∠n=180° > ∠m=180°-∠n > ∠m=180°-60°=120°.

4. 360°. the sum of the exterior angles of an equilateral triangle is ∠m+∠r+∠x=120°+120°+120°=360°. the exterior angles of any triangle always add 360°.

5: 20

step-by-step explanation:

4.28095238095 that is the answer