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Chapter 4: Q11. (page 165)

Find the measure of each numbered angle.

Short Answer

Expert verified

The angles are:

m鈭�5=90鈭�m鈭�6=54鈭�m鈭�7=36鈭�m鈭�8=54鈭�

Step by step solution

01

- Consider the diagram. 

Here, AB鈭�CD.

02

- Show the calculation.

Since, AB鈭�CD,

Here, m鈭�5=m鈭�F=90掳, since they are corresponding angles, where FE is the transversal and AB is parallel to CD.

m鈭�5+m鈭�6+m鈭�GEC=180掳 鈥︹�� [linear angles]

That implies,

m鈭�6+90鈭�+36鈭�=180鈭�m鈭�6+126鈭�=180鈭�

Subtract 126掳 from each side, then,

m鈭�6=180鈭�鈭�126鈭�m鈭�6=54鈭�

Now, m鈭�7=m鈭�6=36掳, since they are vertically opposite angles, where GE is the transversal and AB is parallel to CD.

And m鈭�8=m鈭�GEC=54掳, since they are vertically opposite angles, where GE is the transversal and AB is parallel to CD.

03

- State the conclusion.

Therefore,

m鈭�5=90鈭�m鈭�6=54鈭�m鈭�7=36鈭�m鈭�8=54鈭�

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Most popular questions from this chapter

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to 螖ABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

Draw and label a diagram. List, in terms of the diagram, what is given and what is to be proved. Then write a two-column proof.

In an isosceles triangle, if a segment is drawn from the vertex of the angle between the congruent sides to the midpoint of the opposite side, then congruent triangles are formed.

For the following figure, do the SAS postulates justify that the two triangles are congruent?

Find the values ofx and y.

27. ln equiangular 螖ABC,AB=4x-y,BC=2x+3y and AC=7.

OR炉is a common side of two congruent quadrilaterals.

Complete: quad. NERO鈮�quad ?炉.
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