Reasoning with Angles

• a vertically opposite angle and therefore equal
• an alternate angle and therefore equal
• a vertically opposite angle and therefore equal

• a vertically opposite angle and therefore equal
• a corresponding angle and therefore equal
• an alternate angle and therefore equal

angle c is ​ (a)   because ​ ​ (b)  

• a vertically opposite angle and therefore equal
• an interior angle and therefore adds to 180º.
• an alternate angle and therefore equal

angle d is ​ (a)   because ​ ​ (b)  

• a vertically opposite angle and therefore equal
• a corresponding angle and therefore equal.
• an alternate angle and therefore equal

angle a is ​ (a)   because ​ ​ (b)  

• a vertically opposite angle and therefore equal
• an alternate angle and therefore equal.
• a corresponding angle and therefore equal

angle b is ​ (a)   because ​ ​ (b)  

• a vertically opposite angle and therefore equal
• a corresponding angle and therefore equal.
• an alternate angle and therefore equal

angle c is ​ (a)   because ​ ​ (b)  

• a vertically opposite angle and therefore equal
• a corresponding angle and therefore equal.
• an alternate angle and therefore equal

angle d is ​ (a)   because ​ ​ (b)  

• a vertically opposite angle and therefore equal
• an interior angle and therefore adds to 180º
• an alternate angle and therefore equal

angle d is ​ (a)   because ​ ​ (b)  

• a vertically opposite angle and therefore equal
• a corresponding angle and therefore equal
• an alternate angle and therefore equal

Find the value of 𝑥 in the diagram, stating any angle rules you use.