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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掳and 50掳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鈭�ADC+m鈭�DAC+m鈭�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鈭�CAB=40掳.

04

Step 4. Apply an angle sum theorem.

Consider a right-angled triangle ABC, such that,

m鈭�CAB+m鈭�ABC+m鈭�BCA=180

40+90+y=180

y=180鈭�130

=50

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

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