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III. Regents Questions

9) In the diagram below, ΔLMO is isosceles with LO=MO.

If m∠L=55 and m∠NOM=28, what is m ∠N ?

(1) 27

(2) 28

(3) 42

(4) 70

10) In the diagram below of isosceles ΔABC, the measure of vertex angle B is 80⁰. If AC extends to point D, what is m∠BCD?

(1) 50

(2) 80

(3) 100

(4) 130

11) In the diagram below of ΔA B C, AB = AC, m ∠A=3x, and m∠B=x+20. What is the value of x?

(1) 10

(2) 28

(3) 32

(4) 40

III Regents Questions 9 In the diagram below ΔLMO is isosceles with LO MO If m L 55 and m NOM 28 what is m

Answer :

The measures on the isosceles triangles are given as follows:

9)

10) m < BCD = 130º. (option 4).

11) x = 28º. (option 2).

What is isosceles triangle?

An isosceles triangle is a triangle that has two equal side lengths, hence it also has two equal angle measures.

For item 9, triangle LMO is isosceles, with two angles of 55º, hence the measure of angle M on triangle LMO is given as follows:

(sum of the internal angles of a triangle is of 180º).

On triangle NMO, the measure is given as follows:

(as it is external to the angle of triangle LMO).

Hence the measure of angle N is given as follows:

For item 10, the base angle is given as follows:

2x + 80 = 180

2x = 100

x = 50º.

Hence the exterior angle measure is given as follows:

m < BCD = 180 - 50

m < BCD = 130º.

(angle is supplementary with it's exterior).

For item 11, if AB = AC, the base angle is of (x + 20)º, hence the value of x is obtained as follows:

3x + 2(x + 20) = 180

5x + 40 = 180

5x = 140

x = 140/5

x = 28º.

More can be learned about isosceles triangles at https://brainly.com/question/23986525

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