# In parallelogram abcd, the angle abc is 150 °. The bisector of the bad angle intersects side bc at point L. Find the angle ALC.

January 13, 2021 | education

| Let’s find the values that are needed to solve the problem. Determine the value of the angle BAD:

Angle CBA + Angle BAD = 180;

150 + angle BAD = 180;

angle BAD = 180 – 150 = 30 degrees.

The bisector divides the angle in half, so the angle BAL = angle LAD = 30: 2 = 15.

Consider triangle ABL:

angle ABL + angle BAL + angle BLA = 180;

150 + 15 + angle BLA = 180;

angle BLA = 180 – 150 – 15;

BLA angle = 15 degrees.

Let’s find the required angle:

angle BLA + angle ALC = 180;

15 + angle ALC = 180;

angle ALC = 180 – 15;

angle ALC = 165.

Answer: 165 degrees.