Question

Use the image below to determine the type of angle pair,

relationship, value of x, and the missing angle measure.
15x + 5
14x +11

Answer 1

Name: alternate exterior angles

Relationship: they are congruent. (15x + 5)° = (14x + 11)

Value of x: 6

Missing angle measures: 95°

Explanation:

The two angles given, (15x + 5)° and (14x + 11)°, are both alternate exterior angles that lie outside the parallel lines, with each lying in the opposite direction to each other on the transversal that crosses the parallel lines. This type of angle pair is: alternate exterior angles.

The relationship that exist between this type of angle pair is: alternate exterior angles are congruent. Therefore, (15x + 5)° = (14x + 11)°.

Use the above stated equation derive from the relationship to find the value of x:

`15x + 5 = 14x + 11`

Combine like terms

`15x + 5 - 14x = 14x + 11 - 14x` (Subtraction property of equality)

`x + 5 = 11`

`x + 5 - 5 = 11 - 5` (Subtraction property of equality)

`x = 6`

Plug in the value of x into the expression of each missing angle to find their measures:

(15x + 5)° = 15(6) + 5 = 90 + 5 = 95°

(14x + 11)° = 14(6) + 11 = 84 + 11 = 95°