m∠5=112° and m∠8=(2x+8)°. What equation will solve for x?

(2 points)
___x°+___°=___°

1 answer

To solve for \( x \), we will establish that angles \( 5 \) and \( 8 \) are related in some way, but without additional information about how these angles are positioned (for example, if they are supplementary, complementary, or vertical angles), we can only create a general equation.

Assuming angles \( 5 \) and \( 8 \) are supplementary (the most common case when two angles add up to \( 180^\circ \)), we can formulate the equation as follows:

Given:

  • \( m∠5 = 112^\circ \)
  • \( m∠8 = (2x + 8)^\circ \)

The equation for supplementary angles would be: \[ m∠5 + m∠8 = 180^\circ \]

Substituting the known values, we get: \[ 112^\circ + (2x + 8)^\circ = 180^\circ \]

To express this in the requested format of ___x° + ___° = ___°, we will rearrange it:

  1. Combine like terms: \[ 2x + 112 + 8 = 180 \]

This simplifies to: \[ 2x + 120 = 180 \]

Thus, the equation to solve for \( x \) would be: \[ 2x + 120 = 180 \]

Now we can fill in the blanks:

  • \( ___x° + ___° = ___° \) would correspond to:
  • \( 2x + 120 = 180 \)

So the completed statement is: 2x° + 120° = 180°.