Question

g.co.c.9 worksheet #1

1. circle (t)rue or (f)alse.

a) $\angle 1 \cong \angle 4$ t or f
c) $\angle 3 \cong \angle 5$ t or f
e) $\angle 2 \cong \angle 10$ t or f
g) $\angle 12 \cong \angle 14$ t or f
i) $m\angle 11 + m\angle 15 = 180^\circ$ t or f
j) $m\angle 1 + m\angle 8 = 180^\circ$ t or f
b) $\angle 6 \cong \angle 16$ t or f
d) $\angle 4 \cong \angle 5$ t or f
f) $\angle 9 \cong \angle 15$ t or f
h) $\angle 9 \cong \angle 11$ t or f

1. solve for the unknown values.

a) $x = \underline{\quad\quad\quad}$
d) $x = \underline{\quad\quad\quad}$
b) $x = \underline{\quad\quad\quad}$
e) $x = \underline{\quad\quad\quad}$
c) $x = \underline{\quad\quad\quad}$
f) $x = \underline{\quad\quad\quad}$

Explanation:

For Question 15 (True/False):

Use angle relationships (vertical, alternate interior, corresponding, same-side interior) from parallel lines cut by transversals:
a) $\angle1$ and $\angle4$ are vertical angles, so congruent.
b) $\angle6$ and $\angle16$ have no congruent relationship (not corresponding/alternate).
c) $\angle3$ and $\angle5$ are same-side interior angles, supplementary not congruent.
d) $\angle4$ and $\angle5$ are alternate interior angles, so congruent.
e) $\angle2$ and $\angle10$ are corresponding angles, so congruent.
f) $\angle9$ and $\angle15$ have no congruent relationship.
g) $\angle12$ and $\angle14$ are alternate interior angles, so congruent.
h) $\angle9$ and $\angle11$ are vertical angles, so congruent.
i) $\angle11$ and $\angle15$ are same-side interior angles, so supplementary.
j) $\angle1$ and $\angle8$ are alternate exterior angles, congruent (not supplementary).

a) Step1: Set angles equal (corresponding)

$3x + 16 = 5x - 10$

a) Step2: Rearrange to solve for x

$16 + 10 = 5x - 3x \implies 26 = 2x \implies x = \frac{26}{2}$

b) Step1: Set angle equal to supplement

$8x - 4 = 180 - 160$

b) Step2: Simplify and solve for x

$8x - 4 = 20 \implies 8x = 24 \implies x = \frac{24}{8}$

c) Step1: Set angles equal (corresponding)

$2x + 13 = 3x + 17$

c) Step2: Rearrange to solve for x

$13 - 17 = 3x - 2x \implies x = -4$

d) Step1: Set angle equal to supplement

$4x + 32 = 180 - 172$

d) Step2: Simplify and solve for x

$4x + 32 = 8 \implies 4x = -24 \implies x = \frac{-24}{4}$

e) Step1: Set angles equal (corresponding)

$5x - 7 = 109$

e) Step2: Simplify and solve for x

$5x = 109 + 7 \implies 5x = 116 \implies x = \frac{116}{5}$

f) Step1: Set angle equal to supplement

$3x + 16 = 180 - 118$

f) Step2: Simplify and solve for x

$3x + 16 = 62 \implies 3x = 46 \implies x = \frac{46}{3}$

Answer:

a) T
b) F
c) F
d) T
e) T
f) F
g) T
h) T
i) T
j) F

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For Question 16 (Solve for x):