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Chapter 4: Q3. (page 165)

Complete each sentence with the most appropriate word, phase or value.

BD鈫�bisects 鈭�ABC,m鈭�ABC=5x鈭�4and m鈭�CBD=2x+10. 鈭�ABCis a(n) ________ angle.

Short Answer

Expert verified

The answer is Obtuse Angle.

Step by step solution

01

Step 1. State the property of bisector.  

There are two properties of a bisector:

1. Any point on the bisector of an angle is equidistant from the sides of the angle.

2. In a triangle, the angle bisector divides the opposite side in the ratio of the adjacent sides.

02

Step 2. State the explanation.

By using the property of the bisector,

m鈭�ABC=2m鈭�CBD5x鈭�4=2(2x+10)5x鈭�4=4x+205x鈭�4x=20+4x=24

Then,

m鈭�ABC=5(24)鈭�4=116

Since the measure of the angle is greater than 90 degrees but less than 180 degrees, m鈭�ABCis an obtuse angle.

Hence, the blank is filled by the term 鈥淥btuse Angle鈥�.

03

Step 3. State the conclusion.

Therefore, 鈥�BD鈫�bisects 鈭�ABC,m鈭�ABC=5x鈭�4 and m鈭�CBD=2x+10.鈭�ABC is a(n) obtuse 补苍驳濒别鈥�.

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