Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Finding x:

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

We know that the sum of the angles of any triangle will be $180^{\circ}$.

So, we have that $(3x-14)+(3x+9)+77=180$.

Combining like terms on the left gives $6x+72=180$.

Subtracting $72$ from both sides gives $6x=108$.

Dividing both sides by $6$ gives $x=18$.

Finding missing angle measures:

$\angle ACB=3x-14=3(18)-14=54-14=40$.

$\angle ABC=3x+9=3(18)+9=54+9=63$.

So, $\angle ACB=40^{\circ}$ and $\angle ABC=63^{\circ}$ and we're done!

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