ABCD is a cyclic quadrilateral in which angle BAD=70,angle ADC=80 and angle ABD=55,AC and BD intersect at M,find angle CMD
ABCD is a cyclic quadrilateral . if BAD=65°,ABD=70°,BDC=45°,then find the value of ABC
To find angle CMD in the given cyclic quadrilateral ABCD, we need to use some properties of cyclic quadrilaterals.
Step 1: Draw a diagram.
First, let's draw a rough sketch of what the situation looks like. Draw a quadrilateral ABCD, where angle BAD is 70 degrees, angle ADC is 80 degrees, and angle ABD is 55 degrees. Intersect AC and BD at point M.
Step 2: Understand the properties of cyclic quadrilaterals.
In a cyclic quadrilateral, the opposite angles sum up to 180 degrees. In other words, for any cyclic quadrilateral ABCD, we have:
angle BAD + angle BCD = 180 degrees
angle ADC + angle ABC = 180 degrees
Step 3: Calculate angle CMD.
Now, we can find angle CMD. Since ABCD is a cyclic quadrilateral, we know that:
angle BAD + angle BCD = 180 degrees (Property of cyclic quadrilaterals)
angle BAD = 70 degrees (Given)
angle BCD = angle CMD (Opposite angles in a cyclic quadrilateral)
Substituting the given angle BAD (70 degrees) and the fact that angle BCD = angle CMD into the equation above, we get:
70 + angle CMD = 180
Subtracting 70 from both sides of the equation, we find:
angle CMD = 110 degrees
Therefore, angle CMD is equal to 110 degrees.