Grade 12 Geometry problems

measure of angle BAC = (180 - 36)/2 = 72 degres : isosceles triangle measure of angle BOC = 2 * measure of angle BAC = 144 degrees

Draw a line BO, which bisects angle ABC. BO and CO have identical lengths as the radii of a circle, so triangle BOC is isoceles. Angle OBC and OCB are equal, and half of the given 36 degrees. The interior angles of a triangle total to 180 degrees, so 180-18-18=144.

Since sides AB and CB are equal in length hence the angles opposite to these sides will also be equal. <BAC=<BCA=x ,so 36+2x=180 ,so x=72 Now BOC is the central angle for the inscribed angle BAC.According to the theorem,the central angle is twice that of the inscribed angle.So,BOC=2BAC BOC=2*72 BOC=I44 degrees.

use your brain

BAC=ACB=(180°-36°)/2;
BAC=72°;
AOC=BAC*2 ;
Explanation:
BAC is the periphery angle of the circle, and we know that central angle = periphery * 2;
AOC=144°

It is given that Ac = Bc

=> Measure of angle BAC = angle ABC

Let angle Bac and Abc be x

BY Angle sum property of a triangle

36 + x + x = 180

=> 36 + 2 x = 180

=> 2x = 144

=> x = 72=Angle BAC

Angle formed int the center of the circle is twice the angle formed on the circumference of it.

=> measure of Angle BOC = 2 . measure of angle BAC

=> Angle BOC = 2 . 72

=> BOC = 144

Daa easy measure of angle BAC = (180 - 36)/2 = 72 degres : isosceles triangle measure of angle BOC = 2 * measure of angle BAC = 144 degrees