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Chapter 3: Q16 (page 97)

Find the values of x and y.

Short Answer

Expert verified

The values of x and y are 40°and role="math" localid="1638176591854" 30°respectively.

Step by step solution

01

Step 1. Name the figure and highlight angle DCO and angle BCO .

02

Step 2. Apply an angle sum theorem.

Consider a ΔAOB, such that,

m∠BAO+m∠AOB+m∠ABO=18090+m∠AOB+40=180m∠AOB=50

03

Step 3. Apply vertically opposite angles.

From the given figure, it can be observed that ∠AOBand ∠DOCare vertically opposite angles. Therefore, m∠AOB=m∠DOC=50°.

04

Step 4. Apply an angle sum theorem.

Consider a ΔBAC, such that,

m∠BAC+m∠ACB+m∠ABC=18090+y+60=180y=30

05

Step 5. Apply an angle sum theorem.

Consider a ΔDOC, such that,

m∠DOC+m∠DCO+m∠ODC=18050+x+90=180x=40

Therefore, the values of x and y are 40°and 30°respectively.

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