# Angle AOB = 120 degrees. Find the BOC angle if BOC angle: AOC angle = 7: 5.

1 variant of the location of the corners: the angle AOB consists of two angles BOC and AOC, therefore: angle BOC + angle AOC = angle AOB; angle BOC + angle AOC = 120 degrees. According to the condition, the angle BOC: angle AOC = 7: 5. Let x be the coefficient of proportionality, then: angle BOC = 7x; angle AOC = 5x. Thus: 7x + 5x = 120; 12x = 120; x = 120/12 (according to the main property of the “cross to cross” proportion); x = 10. Find the degree measure of the BOC angle: BOC angle = 7x = 7 * 10 = 70 (degrees).

Answer: angle BОС = 70 degrees.

Option 2 of the location of the corners: the angle BОС consists of two angles AOC and AOB, then: angle AOC + angle AOB = angle BОС; angle AOC + 120 degrees = angle AOC; angle BОС – angle AOС = 120 degrees. Let х – proportionality coefficient, then: angle BОС = 7х; angle AOC = 5x. 7x – 5x = 120; 2x = 120; x = 120/2 (in proportion); x = 60. Then the angle BOС = 7x = 7 * 60 = 420 degrees (π + 60).

Answer: angle BОС = 420 degrees.