Answer:
Part 3) ∠G=64°,∠H=64°,∠I=52°
Part 4) ∠J=28°,∠K=115°,∠L=37°
Part 5) ∠M=18°,∠N=90°,∠O=72°
Step-by-step explanation:
we know that
In a triangle the sum of the internal angles must be equal to 180 degrees
Part 3) we know that
In the triangle GHI
∠G+∠H+∠I=180°
substitute the values and solve for x
16x+16x+13x=180°
45x=180°
x=180°/45=4°
therefore
∠G=16x=16(4°)=64°
∠H=16x=16(4°)=64°
∠I=16x=13(4°)=52°
Part 4) we know that
In the triangle JKL
∠J+∠K+∠L=180°
substitute the values and solve for x
(x+8)+(6x-5)+(2x-3)=180°
9x=180°
x=180°/9=20°
therefore
∠J=(x+8)=(20+8)=28°
∠K=(6x-5)=(6*20-5)=115°
∠L=(2x-3)=(2*20-3)=37°
Part 5) we know that
In the triangle MNO
∠M+∠N+∠O=180° ----> equation A
we have
∠N=5∠M -----> equation B
∠O=4∠M ----> equation C
substitute equation B and equation C in equation A
∠M+5∠M+4∠M=180°
10∠M=180°
∠M=180°/10=18°
∠N=5∠M=5(18°)=90°
∠O=4∠M=4(18°)=72°
