Chapter 8, Problem 12CT

To determine

To find: the given angle by identifying the supplementary and complementary angles.

Answer to Problem 12CT

  $m\angle DFE={63}^0,m\angle BFC={51}^0\text{ and }m\angle BFE={141}^0.$

Explanation of Solution

Given:

  

Concept used:

Sum of the two angles are complementary.

If two angles form a linear pair the angles are supplementary, a linear pair form a straight angle which contains ${180}^0$ .

Complementary angles are two angles that, when add up, gives ${90}^0$ degrees.

Like sum of two angle of right triangle other than right angle is ${90}^0$ .

Calculation:

Complementary angles are the pairs $\angle CFD$ , $\angle DFE$ and $\angle AFB$ , $\angle BFC$ .

Supplementary angles are the pairs $\angle AFB$ , $\angle BFE$ and $\angle AFD$ , $\angle DFE$ .

Therefore,

  $m\angle DFE={90}^0-m\angle CFD={90}^0-{27}^0={63}^0.$

Similarly,

  $m\angle BFC={90}^0-m\angle AFB={90}^0-{39}^0={51}^0.$

Similarly,

  $m\angle BFE={180}^0-m\angle AFB={180}^0-{39}^0={141}^0.$

Hence, $m\angle DFE={63}^0,m\angle BFC={51}^0\text{ and }m\angle BFE={141}^0.$