Question

direction: label the illustration with the given. write the equation and sol
complete solutions.
1.
triangle twc is shown, where ( mangle twc=(9x - 16)^{circ} ),
( mangle wct=(x + 11)^{circ} ), and ( mangle ctw=(3x + 2)^{circ} ).
what is the measure of ( angle twc )?
2.
jonah is creating a triangular garden. he has 3 pieces of fencing
that measure 5 feet (ft.), 5 ft., and 11 ft.
does jonah have enough fencing to make a triangular garden?
justify your answer using mathematics.
re of el castillo pyramid is shown with ( \triangle cms ) drawn over
( v ), ( h ), and ( g ) are midpoints of each side of the triangle.
the medians ( overline{gm} ), ( overline{ch} ), and ( overline{sv} ) are shown.
( =(8x + 2) ) meters (m), and ( kg=(\frac{4}{3}x + 7)m ).

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(m\angle TWC+m\angle WCT + m\angle CTW=180^{\circ}\).
Substitute the given angle expressions: \((9x - 16)+(x + 11)+(3x+2)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((9x+x + 3x)+(-16 + 11+2)=180\).
\(13x-3 = 180\).

Step3: Solve for \(x\)

Add \(3\) to both sides: \(13x=180 + 3=183\).
Divide both sides by \(13\): \(x=\frac{183}{13}=15\).

Step4: Find \(m\angle TWC\)

Substitute \(x = 15\) into the expression for \(m\angle TWC\): \(m\angle TWC=(9x-16)^{\circ}\).
\(m\angle TWC=(9\times15 - 16)^{\circ}=(135-16)^{\circ}=119^{\circ}\).

Answer:

\(119^{\circ}\)