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Chapter 3: Q13 (page 97)

Find the values of x and y.

Short Answer

Expert verified

The values of x and y are 40°and 50°respectively.

Step by step solution

01

Step 1. Name the figure and highlight angle DCA and angle ACB.

02

Step 2. Apply an angle sum theorem.

Consider a right-angled triangle DAC, such that,

m∠ADC+m∠DAC+m∠ACD=18050+90+x=180x=40

03

Step 3. Description of step.

From figure it is clear that AB and CD are parallel lines. Therefore, two angles, CAB and DCA are alternate interior angles. Therefore, they are equal, that is, m∠CAB=40°.

04

Step 4. Apply an angle sum theorem.

Consider a right-angled triangle ABC, such that,

m∠CAB+m∠ABC+m∠BCA=180

40+90+y=180

y=180−130

=50

Therefore, the values of x and y are 40°and 50°respectively.

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Most popular questions from this chapter

What do the arrowheads in the diagram tell you?

Exercises 23-29 refer to the diagram in step 2 of exercise 22.

Name five lines that appear to be parallel toAG¯.

Classify each pair of angles as alternate interior angles, same-side interior angles, corresponding angles, or none of these.

∠14and∠16

The blue line is a transversal.

a. Name four pairs of corresponding angles.

b. Name two pairs of alternate interior angles.

c. Name two pairs of same-side interior angles.

d. Name two pairs of angles that could be called alternate exterior angles.

e.

Find the values of xand y
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