The chords of the circle Ad and BC intersect. Find the BAC angle. If the angle adc = 35 °. Angle acb = 65 °

Let us find the measures of the arcs on which the inscribed angles are based, the measures of which are known to us. The measure of the arc is twice the value of the inscribed angle that rests on it. The ADC angle rests on the AC arc => 2 * 35 = 70 °. Similarly, the arc AB = 130 °. The whole circle – 360 ° => the measure of the BC arc (the one where there is no point A) = 360-70-130 = 160 °. The angle BAC rests on the arc BC and is inscribed => angle BAC = 1/2 measure of the arc BC = 160/2 = 80 °.
Answer: 80 °.