Will award brainlist to whoever has all the correct calculations! using the law of cosines, write an algebraic proof to show that the angles in an equilateral triangle must equal 60°. use "∧" to indicate exponents. for example, type a2 as a∧2. (hint: let s be a length of each side and x be the angle measure; then use these variables in the law of cosines.)

Law of cosine:

c² = a² +b² -2ab*cosC.

Because the triangle is equilateral a=b=c=x,

and we can write,

x²=x² +x² -2xx*cosC

x² =2x² -2x²* cos C

-x² = -2x²*cos C

cos C= 1/2,

so m∠C=60⁰.

Because all sides are equal, and across of the equal sides should be equal angles, all angles will be also equal and = 60⁰.

angles 1 and 3 are vertical angles, meaning that they are equal to each other. to solve this you may set angle 1 and 3 equal to each other and just solve for x like

110 = 2x + 10

100 = 2x

50 = x

check:

110 = 2* 50 + 10

110 = 100 + 10

110 = 110

hope this !

~just a girl in love with shawn mendes

the answer is c. hope this !

step-by-step explanation: