Angle Pairs Unit Test

Question

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Question
Two supplementary angles have measures m∠ABC=105°
and m∠CBD=(3x−24)°
. What is the equation to solve for x
? (1 point)
(3x−24)°+
°=

°

Answer 1

To find the equation to solve for $x$ given that angles $\mathrm{\angle }ABC$ and $\mathrm{\angle }CBD$ are supplementary, we start with the definition of supplementary angles. Two angles are supplementary if the sum of their measures is ${180}^{\circ }$.

Given:

• $m\mathrm{\angle }ABC={105}^{\circ }$
• $m\mathrm{\angle }CBD=(3x-24{)}^{\circ }$

Since they are supplementary, we can write the equation as:

$$m\mathrm{\angle }ABC+m\mathrm{\angle }CBD={180}^{\circ }$$

Substituting in the values we have:

$${105}^{\circ }+(3x-24{)}^{\circ }={180}^{\circ }$$

Thus, the equation to solve for $x$ is:

$$105+(3x-24)=180$$

You can simplify and solve this equation to find the value of $x$.