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Chapter 3: Q6 (page 97)

Complete.

If m∠6=52and m∠11=82, then m∠7=?

Short Answer

Expert verified

If m∠6=52and m∠11=82, then m∠7is 30.

Step by step solution

01

Step 2. Apply the definition of supplementary angles.

If the sum of measure of two angles is then they are said to be supplementary angles.

02

Step 3. Description of step.

From the given figure, it can be observed that ∠8and ∠11are supplementary angles. Therefore, the sum of measures of ∠8and ∠11is 180, that is,

m∠8+m∠11=180m∠8+82=180m∠8=98

03

Step 4. Apply an angle sum theorem.

From the given figure, it can be observed that ∠6,∠7and ∠8are interior angles of a triangle. Therefore, the sum of measures of ∠6,∠7and is role="math" localid="1637929488343" ∠8, that is ,

m∠6+m∠7+m∠8=180

04

Step 5. Description of step.

Substitute for m∠6, 98 for m∠6into the expression obtained in step 4 to find the value of m∠7.

m∠6+m∠7+m∠8=180

52+m∠7+98=180

m∠7=30

Therefore, the value of m∠7is 30.

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