Questions: Look at the diagram. Which equation can be used to solve for x ? 13x-14=90 13x-14=180 5x-14=90 5x-14=180 Solve for x x=

Transcript text: Look at the diagram. Which equation can be used to solve for $x$ ? \[ \begin{array}{cc} 13 x-14=90 & 13 x-14=180 \\ 5 x-14=90 & 5 x-14=180 \end{array} \] Solve for $x$ \[ x= \]

Solution

Solution Steps

Step 1: Identify the angles in the diagram

The diagram shows two angles, $ (4x)^\circ $ and $ (9x - 14)^\circ $, that together form a right angle (90 degrees).

Step 2: Set up the equation

Since the two angles form a right angle, their sum is 90 degrees. Therefore, we can write the equation: \[ 4x + (9x - 14) = 90 \]

Step 3: Simplify the equation

Combine like terms and solve for $ x $: \[ 4x + 9x - 14 = 90 \] \[ 13x - 14 = 90 \]

Final Answer

The correct equation to use is: \[ 13x - 14 = 90 \]

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