Q10. Find the measure of each numbere... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 4: Q10. (page 165)

Find the measure of each numbered angle.

Short Answer

Expert verified

The angles are:

$\begin{array}{l} m 鈭� 1 = 75^{鈭�} \\ m 鈭� 2 = 40^{鈭�} \\ m 鈭� 3 = 40^{鈭�} \\ m 鈭� 4 = 65^{鈭�} \end{array}$

Step by step solution

- Consider the diagram.

Here, $A B 鈭� C D$ .

- Show the calculation.

Since, $A B 鈭� C D$ ,

Here, $m 鈭� 4 = m 鈭� C = 65 掳$ , since they are corresponding angles, where AC is the transversal and AB is parallel to CD.

$m 鈭� 3 + m 鈭� A E D = 180 掳$ 鈥︹€� [linear angles]

That implies,

$m 鈭� 3 + 140 掳 = 180 掳$

Subtract $140 掳$ from each side, then,

$\begin{matrix} m 鈭� 3 = 180^{鈭�} 鈭� 140^{鈭�} \\ m 鈭� 3 = 40^{鈭�} \end{matrix}$

Now, $m 鈭� 2 = m 鈭� 3 = 40 掳$ , since they are alternate interior angles, where AE is the transversal and AB is parallel to CD.

$\begin{matrix} m 鈭� 1 + m 鈭� 3 + m 鈭� C = 180^{鈭�} \\ m 鈭� 1 + 40^{鈭�} + 65^{鈭�} = 180^{鈭�} \\ m 鈭� 1 + 105^{鈭�} = 180^{鈭�} \end{matrix}$

Subtract $105 掳$ from each side, then,

$\begin{matrix} m 鈭� 1 = 180^{鈭�} 鈭� 105^{鈭�} \\ m 鈭� 1 = 75^{鈭�} \end{matrix}$

- State the conclusion.

Therefore,

$\begin{array}{l} m 鈭� 1 = 75^{鈭�} \\ m 鈭� 2 = 40^{鈭�} \\ m 鈭� 3 = 40^{鈭�} \\ m 鈭� 4 = 65^{鈭�} \end{array}$

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91影视

Find the measure of each numbered angle.

Short Answer

Step by step solution

- Consider the diagram.

- Show the calculation.

- State the conclusion.

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