If figure 5.17 to the right ABCD is a rectangle.if m (angle BDC)=54 degree then find m (angle ABD) and m (angle CBD).
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To solve for the measures of angles ABD and CBD, we will use the fact that opposite angles in a rectangle are congruent. Given that angle BDC has a measure of 54 degrees and ABCD is a rectangle, we can determine the measures of angles ABD and CBD.
Step 1: Recognize the properties of a rectangle:
- Opposite sides of a rectangle are equal in length.
- Opposite angles of a rectangle are congruent.
- The sum of all angles in a rectangle is 360 degrees.
Step 2: Identify the information given in the problem:
- We know that angle BDC measures 54 degrees.
- We are also given that ABCD is a rectangle.
Step 3: Find the measures of angles ABD and CBD:
- Since angle BDC measures 54 degrees and ABCD is a rectangle, angles ABD and CBD are also 54 degrees each. This is because they are opposite angles in the rectangle.
Therefore, the measure of angle ABD is 54 degrees, and the measure of angle CBD is also 54 degrees.
ABD and BDC are alternate interior angles
ABD and CBD are complementary, since angle C is a right angle