Use each picture or description of a triangle, write and solve an equation in order to find the number of degrees in each angle

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°

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