Question

Carrie drew two acute non-overlapping angles that share a ray and labeled them ADB and BDC.The two angles have the same whole number measure. What is the least possible measure of ADC? What is the greatest possible measure of ADC

Answer 1

Part 1) The least possible measure of angle ADC is 2 degrees

Part 2) The greatest possible measure of angle ADC is 178 degrees

Explanation:

we know that

An acute angle is an angle that measures less than 90 degrees and greater than 0 degrees

Remember that

The two angles have the same whole number measure

so

`m\angle ADB=m\angle BDC`

The measure of angle ADC is equal to

`m\angle ADC=m\angle ADB+m\angle BDC` ---> by Addition Angle Postulate

so

The least possible measure of ADC is for

`m\angle ADB=m\angle BDC=1^o` ----> remember that is a whole number

so

`m\angle ADC=1^o+1^o=2^o`

The greatest possible measure of ADC is for

`m\angle ADB=m\angle BDC=89^o` ----> remember that is a whole number

so

`m\angle ADC=89^o+89^o=178^o`