Angle Measures 0129A8

1. **Problem Statement:** We are given a protractor diagram with rays from point $A$ to points $B$, $C$, $D$, $E$, and $F$. We need to find the measures of angles $m\angle BAC$, $m\angle DAE$, and $m\angle EAC$ and classify each angle based on its measure. 2. **Understanding Angle Classification:** - An **acute angle** measures less than $90^\circ$. - A **right angle** measures exactly $90^\circ$. - An **obtuse angle** measures more than $90^\circ$ but less than $180^\circ$. - A **straight angle** measures exactly $180^\circ$. 3. **Using the Protractor Diagram:** Assuming the protractor is aligned such that ray $AF$ is at $0^\circ$ and angles increase counterclockwise, we read the angle measures for each ray: - $AB$ at $20^\circ$ - $AC$ at $70^\circ$ - $AD$ at $110^\circ$ - $AE$ at $140^\circ$ 4. **Calculate Each Angle:** - $m\angle BAC$ is the angle between rays $AB$ and $AC$: $$m\angle BAC = |70^\circ - 20^\circ| = 50^\circ$$ - $m\angle DAE$ is the angle between rays $AD$ and $AE$: $$m\angle DAE = |140^\circ - 110^\circ| = 30^\circ$$ - $m\angle EAC$ is the angle between rays $AE$ and $AC$: $$m\angle EAC = |140^\circ - 70^\circ| = 70^\circ$$ 5. **Classify Each Angle:** - $m\angle BAC = 50^\circ$ is less than $90^\circ$, so it is an **acute angle**. - $m\angle DAE = 30^\circ$ is less than $90^\circ$, so it is an **acute angle**. - $m\angle EAC = 70^\circ$ is less than $90^\circ$, so it is an **acute angle**. **Final answers:** - $m\angle BAC = 50^\circ$, Classification: Acute angle - $m\angle DAE = 30^\circ$, Classification: Acute angle - $m\angle EAC = 70^\circ$, Classification: Acute angle