Chapter 12, Problem 11CR

a.

To determine

To calculate:Theanglep of triangle ABC.

Answer to Problem 11CR

The anglep of triangleABCis${60}^{\circ }$ .

Explanation of Solution

Given information:

A triangle ABC is ${30}^{\circ }{60}^{\circ }{90}^{\circ }$ triangle with sides AB as 9 and AC as 18.

Calculation:

  

A triangle ABC is ${30}^{\circ }{60}^{\circ }{90}^{\circ }$ triangle. The angle opposite to side 9 is ${30}^{\circ }$ .

The remaining angle $\angle p={60}^{\circ }$ .

b.

To determine

To find: The angle q of a quadrilateral inscribed in a circle.

Answer to Problem 11CR

The angle q is ${83}^{\circ }$ .

Explanation of Solution

Given information:

A quadrilateral inscribed in a circle with one set of opposite angles as ${97}^{\circ }$ and q.

Calculation:

  

When quadrilateral is inscribed in a circle, opposite angles are supplementary.

  $\begin{array}{l}{97}^{\circ }+\angle q={180}^{\circ }\\ \angle q={180}^{\circ }-{97}^{\circ }\\ \angle q={83}^{\circ }\end{array}$

c.

To determine

To calculate: The angle r of a triangle.

Answer to Problem 11CR

The angle r of a triangle is ${50}^{\circ }$ .

Explanation of Solution

Given information:

A measure of exterior angle of triangle is ${72}^{\circ }$ .Triangle with angles r and ${22}^{\circ }$ .

Calculation:

  

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

  $\begin{array}{l}{72}^{\circ }={22}^{\circ }+\angle r\\ \angle r={72}^{\circ }-{22}^{\circ }={50}^{\circ }\end{array}$ .

d.

To determine

To find: The angle sformed by tangents of acircle.

Answer to Problem 11CR

The angle s is ${78}^{\circ }$ .

Explanation of Solution

Given information:

A circle with two tangents.

Measure of major arc $={258}^{\circ }$

Calculation:

  

Measure of minor arc $={360}^{\circ }-{258}^{\circ }={102}^{\circ }$

The sum of the measures of a tangent angle and its minor arc is ${180}^{\circ }$ .

  $\begin{array}{l}\angle s+{102}^{\circ }={180}^{\circ }\\ \angle s={78}^{\circ }\end{array}$