Question

Amy claims that m∠4+m∠5=m∠10+m∠9. Is Amy correct? Use appropriate mathematical language to justify your response. Enter your answer and your justification in the space provided.

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Answer 1

By using property of transversal line and parallel lines( interior angles and linear angle sum measures the same.)

Explanation:

Given:

m∠4+m∠5=m∠10+m∠9.

To Find :

Proper mathematical proof to it

Solution:

Consider a fig as shown in fig (Refer the attachment)

Draw two parallel and 2 transversal and label each angle as 1 ,2,3,4 ,5,6,7,8 upto 16 .

We get that

angle 4th and angle 5th are the interior and alternate angles

i.em∠4 and m∠5 both are interior alternate angles

they add up to 180 degree.

And angle 10 and angle 9 are linear angle

and then also add up to 180

m∠4+m∠5=180

and also m∠10+m∠9=180

Hence by transitive law a=c and b= c then a=b

So m∠4+m∠5=m∠10+m∠9.

hence proved .