Answer:
angle HMS = 62 degrees
x = 13 degrees
AT = 28
Explanation:
angle SHM and angle HMS are both inside the triangle SMH.
We want to find the angle of HMS. We know that the sum of the angles in the triangle adds up to 180 degrees. There are two angles that we already know.
Angle SHM = 28 (given)
Angle HSM = 90 (because it is a right angle which is always 90 degrees, right angles are formed at two perpendicular lines)
Angle HMS = x (we let angle HMS be a variable as we don't know the value for it)
x + 90 + 28 = 180
x = 62 ddegrees
HMS is 62 degrees
TSA is a right angle in triangle AST because it is formed by two perpendicular lines. Right angles always equal 90 degrees.
10x - 40 = 90
10x = 130
x = 13 degrees
AT and HT are both congruent sides. We know this because the figure we are given is a kite. In a kite, we have two pairs of sides that are congruent to each other. HT is congruent to AT while HM is congruent to AM.
So,
8x - 4 = 2x + 20
Subtraact 2 x from both sides
6x - 4 = 20
Add 4 to both sides
6x = 24
Divide 6 on both sides.
x = 4
Plug x back to AT.
AT = 2(4) + 20 = 28