Answer:
A: m<BOD = 95°
O: m<AOC = 75°
R: m<AOD = 113°
T: m<GUH = 61°
M: m<GUI = 92°
E: m<EUF = 37°
F: m<EUI = 160°
K: m<MAN = 30°
I: m<LAM = 40°
S: m<KAM = 80°
H: m<JAN = 140°
N: m<KAN = 110°
✅I STINK THEREFORE I HAM
Explanation:
A: m<BOD = 57° + 38° = 95°
O: m<AOC = 18° + 57° = 75°
R: m<AOD = 18° + 57° + 38° = 113°
T: m<FUG = 31°, since, FUG ≅ HUI, therefore, m<HUI = 31°
m<FUI = 123°
m<GUH = m<FUI - (m<FUG + m<HUI)
m<GUH = 123° - (31° + 31°)
m<GUH = 61°
M: m<GUI = m<GUH + HUI
m<GUI = 61° + 31°
m<GUI = 92°
E: m<EUH = 129° (given)
m<EUF = m<EUH - (m<FUG + m<GUH)
m<EUF = 129° - (31° + 61°)
m<EUF = 37°
F: m<EUI = m<EUF + m<FUG + m<GUH + m<HUI
m<EUI = 37° + 31° + 61° + 31°
m<EUI = 160°
K: since <JAK ≅ <MAN, and m<JAK is given as 30°, therefore,
m<MAN = 30°
I: m<JAM = 110° (given), m<JAK = 30° (given)
Since <KAL ≅ <LAM, therefore,
m<LAM = ½(m<JAM - m<JAK)
m<LAM = ½(110° - 30°)
m<LAM = 40°
S: m<KAM = m<KAL + m<LAM
Since <KAL ≅ <LAM, therefore,
m<KAM = 40° + 40°
m<KAM = 80°
H: m<JAN = m<JAK + m<KAL + m<LAM + m<MAN
m<JAN = 30° + 40° + 40° + 30°
m<JAN = 140°
N: m<KAN = m<KAL + m<LAM + m<MAN
m<KAN = 40° + 40° + 30
m<KAN = 110°
Place the letters on the appropriate lines given to match the angle measure we've cakcukated, to figure out the joke.
✅We would have:
I STINK THEREFORE I HAM