Where it says “Exercises.”
Is number 1 = 90 ?

Yes you are correct. The diagonals of any kite are perpendicular.

This can be proven by showing that triangle KGH is congruent to triangle KJH through the SSS congruence theorem. From there you break up the triangles focusing on triangle JRK and triangle GRK, now using the SAS rule to conclude that angle JRK = angle GRK. Since those are a linear pair, those angles must be right angles.

Side note: A kite is defined to be any quadrilateral in which it has two pairs of adjacent congruent sides. Not all four sides are the same length though (otherwise we would have a rhombus).

any options?

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1