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CAN SOMEONE HELP. i will give 150 points if some one can explain and solve you have to find the missing angle measures.

CAN SOMEONE HELP I Will Give 150 Points If Some One Can Explain And Solve You Have To Find The Missing Angle Measures class=

Sagot :

danielgeyfman

Answer:

\angle ACB=40^{\circ}, \angle ABC=63^{\circ}

Step-by-step explanation:

Finding x:

We know that [tex]\angle DAB=180^{\circ}[/tex], because it's a straight line. So, [tex]\angle CAB=180^{\circ}-103^{\circ}=77^{\circ}[/tex].

We know that the sum of the angles of any triangle will be [tex]180^{\circ}[/tex].

So, we have that [tex](3x-14)+(3x+9)+77=180[/tex].

Combining like terms on the left gives [tex]6x+72=180[/tex].

Subtracting [tex]72[/tex] from both sides gives [tex]6x=108[/tex].

Dividing both sides by [tex]6[/tex] gives [tex]x=18[/tex].

Finding missing angle measures:

[tex]\angle ACB=3x-14=3(18)-14=54-14=40[/tex].

[tex]\angle ABC=3x+9=3(18)+9=54+9=63[/tex].

So, [tex]\angle ACB=40^{\circ}[/tex] and [tex]\angle ABC=63^{\circ}[/tex] and we're done!

Note: [tex]\angle ACB+\angle ABC=\angle CAD[/tex]. Coincidence? If not, try and prove it!

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