Question

name
date
use the diagram to the right to answer #18 - 21. 3 pts each

1. ( x = )
2. ( m angle a=)
3. ( m angle b=)
4. ( m angle c=)
5. use the diagram to the right to answer the following questions. 2 pts each

( m angle 1=)( m angle 2=)( m angle 3=)( m angle 4=)
extra credit solve for ( x ) and ( y ) that will make both sets of lines parallel
show all work for credit! (3 pts each)
( 2 x + 11 = 3 y - 5 )
( 5 y - 7 = x + 16 )

Explanation:

Step1: Solve for \( x \) in the triangle (Question 18)

The sum of angles in a triangle is \( 180^{\circ} \).
So, \( (4x - 1)+(3x + 21)+(4x + 6)=180 \)
Combine like terms: \( 4x-1+3x + 21+4x + 6=180 \)
\( 11x+26 = 180 \)
Subtract 26 from both sides: \( 11x=180 - 26=154 \)
Divide by 11: \( x=\frac{154}{11}=14 \)

Step2: Find \( m\angle A \) (Question 19)

Substitute \( x = 14 \) into \( (4x-1) \)
\( m\angle A=4\times14-1=56 - 1=55^{\circ} \)

Step3: Find \( m\angle B \) (Question 20)

Substitute \( x = 14 \) into \( (3x + 21) \)
\( m\angle B=3\times14+21=42+21=63^{\circ} \)

Step4: Find \( m\angle C \) (Question 21)

Substitute \( x = 14 \) into \( (4x + 6) \)
\( m\angle C=4\times14+6=56+6=62^{\circ} \)

Step5: Solve for angles in the second diagram (Question 22)

• \( m\angle1 \): Using the exterior - angle property (the exterior angle is equal to the sum of the two non - adjacent interior angles). \( m\angle1=63^{\circ}+15^{\circ}=78^{\circ} \)
• \( m\angle2 \): Since \( \angle1 \) and \( \angle2 \) are supplementary (linear pair), \( m\angle2 = 180^{\circ}-78^{\circ}=102^{\circ} \)
• \( m\angle3 \): Right - angle, \( m\angle3 = 90^{\circ} \)
• \( m\angle4 \): In the right - triangle with \( \angle3 = 90^{\circ} \) and one angle \( 63^{\circ} \), \( m\angle4=180^{\circ}-(90^{\circ}+63^{\circ})=27^{\circ} \)

Answer:

1. \( 14 \)
2. \( 55^{\circ} \)
3. \( 63^{\circ} \)
4. \( 62^{\circ} \)
5. \( m\angle1 = 78^{\circ} \), \( m\angle2 = 102^{\circ} \), \( m\angle3 = 90^{\circ} \), \( m\angle4 = 27^{\circ} \)