Complete the following statements to prove that ∠ikl and ∠jld are supplementary angles. it is given that ∠eij ≅ ∠gji. also, ∠eij ≅ ∠ikl and ∠gji ≅ ∠jlk, as they are corresponding angles for parallel lines cut by a transversal. by the definition of congruent angles, m∠eij = m∠gji, m∠eij = m∠ikl, and m∠gji = m∠jlk. so, m∠ikl = m∠jlk by the . angle jlk and ∠jld are supplementary angles by the , so m∠jlk + m∠jld = 180°. by the , m∠ikl + m∠jld = 180°. therefore, ∠ikl and ∠jld are supplementary angles by definition.

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step-by-step explanation:

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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