4. In the following diagram, it is known that ZEHG is a right angle, MZEHF = x +1 and M2GHF = 5x+5. Find the value of x, the numerical values of mzEHF and MZGHF , and mark them on the diagram.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.2: The Law Of Cosines
Problem 3E
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4. In the following diagram, it is known that ZEHG is a right angle, m/EHF = x+1 and m2GHF =5x+5.
Find the value of x, the numerical values of mZEHF and m/GHF, and mark them on the diagram.
Straight angles are extremely important in geometry. When two lines intersect, they form multiple (four)
angles. In the diagram below, lines GM and FH intersect at E. If any of the four angles formed is given,
all other three can be found quickly. Fill in the table below.
F
MLGEF
MZFEM
MZMEH
MZHEG
120
150
G
25
45°
H
REASONING
6. Vertical Angles: Vertical angles are angles that are opposite of each other when two straight lines cross. In
the diagram in #5, ZGEF and ZMEH are a pair of vertical angles while ZFEM and ZHEG are also.
(a) Given the results of your calculations in #5,
(b) Why do you think this occurs?
what can you say about the measure of vertical
angles?
COMMON CORE GEOMETRY, UNIT #1–ESSENTIAL GEOMETRIC TOOLS AND CONCEPTS-LESSON #3
Transcribed Image Text:4. In the following diagram, it is known that ZEHG is a right angle, m/EHF = x+1 and m2GHF =5x+5. Find the value of x, the numerical values of mZEHF and m/GHF, and mark them on the diagram. Straight angles are extremely important in geometry. When two lines intersect, they form multiple (four) angles. In the diagram below, lines GM and FH intersect at E. If any of the four angles formed is given, all other three can be found quickly. Fill in the table below. F MLGEF MZFEM MZMEH MZHEG 120 150 G 25 45° H REASONING 6. Vertical Angles: Vertical angles are angles that are opposite of each other when two straight lines cross. In the diagram in #5, ZGEF and ZMEH are a pair of vertical angles while ZFEM and ZHEG are also. (a) Given the results of your calculations in #5, (b) Why do you think this occurs? what can you say about the measure of vertical angles? COMMON CORE GEOMETRY, UNIT #1–ESSENTIAL GEOMETRIC TOOLS AND CONCEPTS-LESSON #3
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