Question

find each angle measure.

1. m∠1
2. m∠2
3. m∠abc
4. m∠def
5. in the diagram, roads a and b are parallel.

what is the measure of ∠pqr?
use the diagram of a staircase railing for exercises 19 - 20. $overline{ag}paralleloverline{cj}$ and $overline{ad}paralleloverline{fj}$.

1. which is a true statement about the measure of ∠dcj?

a it equals 30°, by the alternate interior angles theorem.
b it equals 30°, by the corresponding angles postulate.
c it equals 50°, by the alternate interior angles theorem.
d it equals 50°, by the corresponding angles postulate.

1. which is a true statement about the value of n?

a n = 25, by the alternate interior angles theorem
b n = 25, by the same - side interior angles theorem
c n = 35, by the alternate interior angles theorem
d n = 35, by the same - side interior angles theorem

Explanation:

Answer:

(14) \( 133^{\circ} \)
(15) \( 119^{\circ} \)
(16) \( 83^{\circ} \)
(17) First solve \( 8x - 34=5x + 2 \), \( 8x-5x=2 + 34 \), \( 3x=36 \), \( x = 12 \). Then \(m\angle DEF=(5x + 2)^{\circ}=(5\times12 + 2)^{\circ}=62^{\circ}\)
(18) Since \(x + 40=2x-22\), \(2x-x=40 + 22\), \(x = 62\). \(\angle PQR=(x + 40)^{\circ}=102^{\circ}\)
(19) C. It equals \(50^{\circ}\), by the Alternate Interior Angles Theorem.
(20) D. \(n = 35\), by the Same - Side Interior Angles Theorem.