Solve for x. what are the measures of the two smaller angles? show your work

x = 7

The two smaller angles are 23° each

Step-by-step explanation:

x + 16 = 4x - 5 (vertical angles are congruent)

x + 16 - 4x = 4x - 5 - 4x (subtraction property of equality)

-3x + 16 = - 5 (simplification)

-3x + 16 - 16 = -5 - 16 (subtraction property of equality)

-3x = -21 (simplification)

-3x/-3 = -21/-3 (division property of equality)

x = 7 (simplification)

✔️Measure of the two smaller angles:

Plug in the value of x

x + 16 = 7 + 16 = 23°

4x - 5 = 4(7) - 5 = 28 - 5 = 23°

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)