What is the measure of angle BCD? m∠BCD =___ degrees

Solution:

Whenever two rays join together they form an angle and the angle subtended by two rays in opposite directions is called a straight angle.

In geometry, a straight angle is an angle whose vertex point has a value of 180 degrees.

Since BA is a straight line, we can write as:

∠BAD + 25° = 180°  

∠BAD = 180° - 25° = 155°

Similarly,

∠ADC = 180° - 149° = 31°

∠CBA = 180° - 146° = 34°

Hence, from angle sum property of quadrilateral, 

∠BCD = 360° - 155° - 31° - 34° = 140°

What is the measure of angle BCD? m∠BCD =___ degrees

Summary:

The measure of angle BCD is 140°