If △CAT∼△DOG
m∠C=105∘
m∠T=(x+11)∘
m∠O=3x∘
Find m∠O

m∠O = 48°

Explanation:
If △CAT∼△DOG, then:
m∠C = m∠D
m∠A = m∠O
m∠T = m∠G

In a triangle, the sum of all interior angles is 180°, so:
m∠C + m∠A + m∠T = 180°

Substitute information given in the problem:
105° + m∠A + (x + 11)° = 180°

Since m∠A = m∠O, and m∠O = 3x°, then m∠A = 3x°
105° + 3x° + (x + 11)° = 180°

Simplify and isolate ‘x’.
105° + 3x° + x° + 11° = 180°
116° + 4x° = 180°
4x° = 64°
x = 16°

Solve for m∠O using x = 16° and m∠O = 3x°.
m∠O = 3(16°)
m∠O = 48°

Therefore, the measure of ∠O is 48°.