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Chapter 10: Q14. (page 378)

On your paper, draw two angles roughly like those shown. Then for Exercise 11-14construct an angle having the indicated measure. 180-2y

Short Answer

Expert verified

The figure is,

Step by step solution

01

Step 1. Given information.

The angle to draw is 180-2y.

Angles xand y can be constructed as,

02

Step 2. Concept.

To construct 180-2y, consider the following ways-

Draw a line CE.

Mark the point Bon line CE.

Draw angle yfrom point B.

Place the compass vertex on the angle’s vertex B. and mark that point as s.

With centre s,draw an arc and mark that point as H on the angle y.

With centre Hand without changing the radius of the compass,

draw another arc and mark that point as G.

Draw a line from Bto where the arcs intersect.

Mark as ABand BD.

03

Step 3. Apply angle sum property.

According to the angle sum property,

∠ABE=2y and ∠ABC=180-2y

04

Step 4. Construct the figure. 

The figure is,

Therefore, the required construction is ∠ABC=180-2y as shown above.

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Most popular questions from this chapter

Construct an angle with the indicated measure.

45°.

Repeat Exercise 7, but use the SAS method.

These exploratory exercises can be done using a computer with a program that draws and measures geometric figures.

1. Draw any ▵ABC.Draw the bisectors of the angles of the triangle. They should intersect in one point. Draw a perpendicular segment from this point to each of the sides. Measure the length of each perpendicular segment. What do you notice?

On your paper, draw two angles roughly like those shown. Then for Exercise 11-14 construct an angle having the indicated measure. x-y

Using any convenient length for a side, construct an equilateral triangle.
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