Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - 10.2 Triangles - Exercise Set 10.2 - Page 626: 7

Answer

Measurement of angle 1 is\[50{}^\circ \], angle 2 is\[50{}^\circ \], angle 3 is\[80{}^\circ \], angle 4 is\[130{}^\circ \]and angle 5 is\[130{}^\circ \].

Work Step by Step

Compute angle 1 using the fact that angles \[130{}^\circ \] and angle 1 form a straight angle. Therefore, their sum is equal to\[180{}^\circ \]. \[130{}^\circ +m\measuredangle 1=180{}^\circ \] Compute the measurement of angle 1 by subtracting \[{{130}^{{}^\circ }}\]from both the sides of equation. \[\begin{align} & m\measuredangle 1=180{}^\circ -130{}^\circ \\ & m\angle 1=50{}^\circ \\ \end{align}\] Compute the measurement of angle 2 using the fact that angles opposite to the equal sides of isosceles triangle are equal as shown below. \[\begin{align} & m\angle 1=m\angle 2 \\ & m\angle 2=50{}^\circ \\ \end{align}\] According to angle sum property, the sum of all the three angles of a triangle is\[180{}^\circ \]. Compute the measure of angle 2 as follows: Sum of all the three angels of a triangle is\[{{180}^{\circ }}\]as shown below. \[m\angle 1+m\angle 2+m\angle 3=180{}^\circ \] Simplify the equation by substituting the given values as follows: \[\begin{align} & 50{}^\circ +50{}^\circ +m\angle 3=180{}^\circ \\ & m\measuredangle 3+100{}^\circ =180{}^\circ \end{align}\] Compute the measurement of angle 3 by subtracting \[{{100}^{{}^\circ }}\]from both the sides of equation as shown below. \[\begin{align} & m\angle 3=180{}^\circ -100{}^\circ \\ & m\angle 3=80{}^\circ \\ \end{align}\] Compute the measurement of angle 4 using the fact that angles 2 and 4 form a straight angle. Therefore, their sum is equal to\[{{180}^{\circ }}\]as shown below: \[m\measuredangle 2+m\sphericalangle 4=180{}^\circ \] Simplify the equation by substituting the given values as follows: \[50{}^\circ +m\angle 4=180{}^\circ \] Compute the measurement of angle 4 by subtracting \[{{50}^{{}^\circ }}\]from both the sides of equation as shown below. \[\begin{align} & m\angle 4=180{}^\circ -50{}^\circ \\ & m\angle 4=130{}^\circ \\ \end{align}\] Compute the measurement of angle 5 using the fact that vertically opposite angles are equal to each other as shown below. \[\begin{align} & m\angle 5=m\angle 4 \\ & m\angle 5=130{}^\circ \\ \end{align}\]
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