Question

1. if ( mangle2 = 112 ), what is ( mangle7 )?

( mangle7=)

1. select all the true statements given

the figure.
a. ( mangle4 = mangle2 )
b. ( mangle4 = mangle1 + mangle2 )
c. ( mangle4 = 180 - mangle3 )
d. ( mangle4 = mangle1 + mangle2 + mangle3 )
e. ( mangle4 = mangle3 + mangle1 )
for items 7 - 9, use the figure shown.

1. what is ( x )?

(a) 28
(c) 136
(b) 44
(d) 224

1. what is ( y )?

( y=)

1. select all the true statements.

a. ( x = y )
d. ( x + z = 180 )
b. ( x + y = 180 )
e. ( y + z = 180 )
c. ( y = z )

Explanation:

Step1: Find \(x\) (Problem 7)

The sum of angles in a triangle is \(180^{\circ}\). Also, an exterior angle \(x\) of a triangle is equal to the sum of the two non - adjacent interior angles.

$$x = 82^{\circ}+54^{\circ}=136^{\circ}$$

Step2: Find \(y\) (Problem 8)

\(x\) and \(y\) are supplementary angles (they form a linear pair). So \(y = 180^{\circ}-x\)
Since \(x = 136^{\circ}\), then \(y=180 - 136=44^{\circ}\)

Step3: Analyze statements for Problem 9

• Option A: \(x = 136^{\circ}\), \(y = 44^{\circ}\), so \(x

eq y\)

• Option B: \(x + y=136 + 44=180^{\circ}\) (True)
• Option C: \(y = 44^{\circ}\), \(z=x = 136^{\circ}\) (vertical angles), so \(y

eq z\)

• Option D: \(x+z = 136+136

eq180^{\circ}\)

• Option E: \(y + z=44 + 136=180^{\circ}\) (True)

Answer:

1. C. \(136\)
2. \(44\)
3. B. \(x + y = 180\), E. \(y + z = 180\)