Q1. In the diagram,聽UL鈫掆姤MJ鈫� a... [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 2: Q1. (page 58)

In the diagram, $\overset{鈫�}{U L} 鈯� \overset{鈫�}{M J}$ and $m 鈭� J U K = x$ . Express in terms of x the measures of the angles named.
a. $鈭� L U K$
b. $鈭� M U K$

Short Answer

Expert verified

a. The value for a given angle is $90 掳 - x 掳$ .

b. The value for a given angle is $180 掳 - x 掳$ .

Step by step solution

Part a. Step 1. Definition of the right angle.

Basically angles having the measurement of 90掳 are referred to as the right angles these angles are from the perpendicular relation between two lines.

Part a. Step 2. Determine the angles that are right angles and make an equation.

The angles $鈭� L U M$ and $鈭� L U J$ represents the right angles. The provided angle is a part of $鈭� L U J$ so its value can be determined by subtracting the value of $鈭� J U K$ from $鈭� L U J$ . By using this make an equation.

$鈭� L U K = 鈭� L U M - 鈭� L U J$

Part a. Step 3. Determine the value of the given angle.

Substitute the value of $鈭� L U M$ and $鈭� J U K$ into the obtained equation.

$鈭� L U K = 90 掳 - x 掳$

Part b. Step 1. Observe the provided figure.

The provided angle is a part of straight-lineMUJ.

Part b. Step 2. Make an equation.

Every line that is straight having the measurement of 180掳, therefore, the value of provided angle can be determined by subtracting the value of from $鈭� J U K$ the measurement of the straight line. By using this make an equation.

$鈭� M U K = 180 掳 - 鈭� J U K$