In the diagram, ∠CAB is a straight angle. Describe the angle relationship. Write an equation for the angle relationship and solve for x. Check your solution to the equation.
Understand the Problem
The question involves analyzing a geometric relationship involving angles and requires the user to describe the angle relationship, write an equation based on that relationship, and then solve for the variable x.
Answer
$x = 108^\circ$
Answer for screen readers
The value of $x$ is $108^\circ$.
Steps to Solve
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Identify the Angle Relationship
In the diagram, angle $\angle CAB$ is a straight angle, meaning it measures $180^\circ$. The angles $\angle DAC$ and $\angle DAB$ are adjacent, and their measures can be added to find the total. -
Write the Equation
Since $\angle CAB$ and the sum of angles $\angle DAC$ and $\angle DAB$ equal $180^\circ$, we can set up the equation:
$$ x + 72^\circ = 180^\circ $$ -
Solve for x
To isolate $x$, subtract $72^\circ$ from both sides:
$$ x = 180^\circ - 72^\circ $$
Now, calculate:
$$ x = 108^\circ $$ -
Check Your Solution
Substitute $x$ back into the original angle relationship to verify:
$$ 108^\circ + 72^\circ = 180^\circ $$
Since this is true, the solution is confirmed.
The value of $x$ is $108^\circ$.
More Information
In geometry, the concept of supplementary angles states that two angles are supplementary if their measures add up to $180^\circ$. In this problem, we used this principle to find the value of $x$ by leveraging the relationship of the angles involved.
Tips
- Forgetting that a straight angle measures $180^\circ$. Always confirm the total of the angles equals this value.
- Confusing adjacent angles as complementary instead of supplementary. Remember complementary angles sum to $90^\circ$, while supplementary angles sum to $180^\circ$.
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