Answer:
m∠O = 48°
Step-by-step 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°.