Question

1. 13) 16) find m∠h.

Explanation:

1. For problem 13:

• Recall the exterior - angle property of a triangle. The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
• In triangle \(BCD\), \(\angle ADC\) is an exterior angle. So, \(\angle ADC=(15x + 5)+(22x+4)\).
• Given that \(\angle ADC = 120^{\circ}\), we can set up the equation:
• Step 1: Combine like terms on the right - hand side of the equation
• \((15x + 5)+(22x+4)=15x+22x + 5 + 4=37x+9\). So the equation becomes \(37x + 9=120\).
• Step 2: Solve for \(x\)
• Subtract 9 from both sides of the equation: \(37x+9 - 9=120 - 9\), which simplifies to \(37x=111\).
• Then divide both sides by 37: \(x=\frac{111}{37}=3\).

1. Since problem 16 has no information about the triangle other than the label \(G\), \(H\) and a non - related number \(352\) written next to it, we assume you want to solve problem 11:

• In triangle \(BCD\), we can use the angle - sum property of a triangle (\(\angle C+\angle D+\angle CBD = 180^{\circ}\)). First, we need to find the relationship between the angles in terms of \(x\).
• Let's assume we use the linear - pair property. If we consider the straight line \(W\), we know that the angle adjacent to \(\angle CBD\) and \(\angle CBD\) form a linear pair. But we can also use the angle - sum property of a triangle directly.
• \(\angle C = 46^{\circ}\), \(\angle D=-1 + 8x\), and the third angle in the triangle (opposite to the side with the expression \(18x + 5\)) can be found using the fact that the sum of angles in a triangle is \(180^{\circ}\).
• \(\angle C+\angle D+(180-(18x + 5))=180\).
• Step 1: Expand and simplify the equation
• \(46+( - 1+8x)+180 - 18x - 5=180\).
• Combine like terms: \((46-1 + 180-5)+(8x-18x)=180\).
• \(220 - 10x=180\).
• Step 2: Solve for \(x\)
• Subtract 220 from both sides: \(-10x=180 - 220=-40\).
• Divide both sides by \(-10\): \(x = 4\).

If we were to answer problem 13:

Step1: Combine like terms

\((15x + 5)+(22x+4)=37x + 9\)

Step2: Solve for \(x\)

\(37x+9 = 120\), then \(37x=111\), \(x = 3\)

Answer:

\(x = 3\)