Answer:
m∠A=92
m∠B=37
m∠C=51
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m∠K=20
m∠L=33
m∠J=127
Step-by-step explanation:
m∠A=7x-6
m∠B=3x-5
m∠C=4x-5
First we have to solve for x, since all the angles of a triangle sum up to 180° knowing this we can set up an equation:
(7x-6)+(3x-5)+(4x-5)=180
7x-6+3x-5+4x-5=180
14x-16=180
14x=196
x=14
Now to find each angle measure we substitute x for our found value.
m∠A=7(14)-6=92
m∠B=3(14)-5=37
m∠C=4(14)-5=51
To double check our answer lets sum up our measures.
92+37+51=180
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This method can also be applied to #10 except we assign the x value ourselves. Lets have m∠K=x.
Now instead of;
m∠L=m∠K+13
m∠J=m∠K*6+7
we have;
m∠L=x+13
m∠J=6x+7
Using the fact that the sum of the angles in a triangle is 180° we can set up an equation:
(x)+(x+13)+(6x+7)=180
x+x+13+6x+7=180
8x+20=180
8x=160
x=20
Now lets plug our x value into our equations for the angles.
m∠K=20
m∠L=20+13=33
m∠J=6(20)+7=127
Now to check lets see if zour angles add up to 180°
127+33+20=180
