In the accompanying diagram of rhombus ABCD, diagonal BD is drawn and measure of angle C = 50 degrees.
find measure of angle ADB
ADB and CBD are both 65 degrees. They bisect angles B and D, which are 130 degrees.
A and C are both 50 degrees.
Draw the rhombus and you should see why these statements can be made.
werawetwe
To find the measure of angle ADB in the rhombus, we need to use the properties of a rhombus and the angle given.
In a rhombus, all four sides are equal in length, and opposite angles are equal. Therefore, angle A is also 50 degrees because it is opposite to angle C.
Now let's focus on triangle ADB. We know that the sum of the interior angles of a triangle is always 180 degrees. So, we can write an equation for triangle ADB as follows:
angle ADB + angle A + angle B = 180 degrees
Substituting the known values:
angle ADB + 50 degrees + 50 degrees = 180 degrees
Combining like terms:
angle ADB + 100 degrees = 180 degrees
To isolate angle ADB, we subtract 100 degrees from both sides:
angle ADB = 180 degrees - 100 degrees
angle ADB = 80 degrees
Therefore, the measure of angle ADB in the rhombus is 80 degrees.