Question

name: tonson
rection: label the illustration with the given. write the equation and
mplete solutions.
1.
triangle twc is shown, where ( mangle twc=(9x - 15)^{circ} ),
( mangle wct=(x + 11)^{circ} ), and ( mangle ctw=(3x + 2)^{circ} ).
what is the measure of ( angle twc )?
2.

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((9x - 15)+(x + 11)+(3x + 2)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((9x+x + 3x)+(-15 + 11+2)=180\).
\(13x-2 = 180\).

Step3: Solve for \(x\)

Add \(2\) to both sides: \(13x=180 + 2=182\).
Divide both sides by \(13\): \(x=\frac{182}{13}=14\).

Step4: Find the measure of \(\angle TWC\)

Substitute \(x = 14\) into the expression for \(\angle TWC\) (\(m\angle TWC=(9x - 15)^{\circ}\)).
\(m\angle TWC=9\times14-15\).
\(m\angle TWC=126-15\).
\(m\angle TWC = 111^{\circ}\).

Answer:

\(111^{\circ}\)