Question

in $\triangle cab$, if $m\angle a = 10x + 9$, $m\angle b = 34^\circ$, and $m\angle c = 97^\circ$, what is the value of $x$? (1 point)

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(m\angle A + m\angle B + m\angle C = 180^\circ\).

Step2: Substitute given angles

Substitute \(m\angle A = 10x + 9\), \(m\angle B = 34^\circ\), and \(m\angle C = 97^\circ\) into the equation:
\((10x + 9) + 34 + 97 = 180\).

Step3: Simplify and solve for x

Simplify the left - hand side: \(10x + 9+34 + 97=10x+(9 + 34+97)=10x + 140\).
Now we have the equation \(10x+140 = 180\).
Subtract 140 from both sides: \(10x=180 - 140=40\).
Divide both sides by 10: \(x=\frac{40}{10}=4\).

Answer:

\(x = 4\)