What are the numerical measures of each angle in the diagram?

29 degrees

151 degrees  

Step-by-step explanation:

m∠1 = 29° = m∠3

m∠2 = 151° = m∠4  

Step-by-step explanation:

m∠1 = (3x -1)° and m∠3 = (2x + 9)°

Since, ∠1 and ∠2 are vertically opposite angles and we know that vertically opposite angles are always equal

⇒ ∠1 = ∠2

⇒ (3x -1)° = (2x + 9)°

⇒ 3x - 2x = 9 + 1

⇒ x = 10

⇒ m∠1 = 3 × 10 - 1

⇒ m∠1 = 29° = m∠3

Now, m∠2 + m∠3 = 180° ( sum of linear pair is 180° )

⇒ m∠2 = 180° - 29°

⇒ m∠2 = 151°

Also, ∠2 = ∠4 ( Vertically opposite angles are always equal)

⇒ m∠2 = 151° = m∠4

step-by-step explanation:

use pothagarean therom

a^2+b^2=c^2 so first ac

acm is a right triangle because c= 90°

and am (the hypotenuse or c) =16+9 =25

but there is not enough info we need another angle or side length