Chapter 3.2, Problem 53SPR

To determine

To determine the given angles.

Answer to Problem 53SPR

  $\begin{array}{l}\angle 6={43}^{\circ }\\ \angle 7={90}^{\circ }\end{array}$

Explanation of Solution

Given information :

  

  $\angle 6\text{ and }\angle 8$ are complementary and $m\angle 8={47}^{\circ }$

From the given figure we can observe that $\angle 6,\angle 7\text{ and }\angle 8$ lie on a straight line hence the angles are suplementary.

Now we get,

  $\begin{array}{l}\angle 6+\angle 7+\angle 8={180}^{\circ }\\ \angle 6+\angle 7+{47}^{\circ }={180}^{\circ }\\ \angle 6+\angle 7={180}^{\circ }-{47}^{\circ }={137}^{\circ }\end{array}$

Now it is given that $\angle 6\text{ and }\angle 8$ are complementary

Hence $\angle 6={90}^{\circ }-{47}^{\circ }={43}^{\circ }$

Now we put the value and determine the value of $\angle 6.$

  $\begin{array}{l}\angle 6+\angle 7={137}^{\circ }\\ \angle 7={137}^{\circ }-{47}^{\circ }={90}^{\circ }\end{array}$

Therefore we get,

  $\begin{array}{l}\angle 6={43}^{\circ }\\ \angle 7={90}^{\circ }\end{array}$