Question

find the measure of the indicated angle that make lines. solve for “x”.

Explanation:

Step1: Identify angle - relationships

For the first four pairs of parallel - lines with a transversal:

• When two parallel lines are cut by a transversal, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary (sum to 180°).
• For the first pair with an 81° angle, if the angles are corresponding or alternate - interior, the indicated angle is 81°.
• For the second pair with a 74° angle, the indicated angle is 74° (assuming corresponding or alternate - interior relationship).
• For the third pair with a 123° angle, if the indicated angle is a corresponding or alternate - interior angle, it is 123°. If it is a same - side interior angle, it is 180°−123° = 57°.
• For the fourth pair with a 108° angle, if the indicated angle is a corresponding or alternate - interior angle, it is 108°. If it is a same - side interior angle, it is 180°−108° = 72°.

Step2: Solve for x in the angle - equations

For the equation 10x + 5=11x−4 (assuming vertical or corresponding/alternate - interior angles are equal):

• First, subtract 10x from both sides:
• 10x + 5−10x=11x−4−10x, which simplifies to 5=x - 4.
• Then, add 4 to both sides: x=5 + 4=9.

For the equation 3 + 23x=22x + 8 (assuming vertical or corresponding/alternate - interior angles are equal):

• Subtract 22x from both sides: 3 + 23x−22x=22x + 8−22x, which gives 3+x=8.
• Subtract 3 from both sides: x=8 - 3=5.

Answer:

For the first four angle - finding problems: 81°, 74°, 123° or 57°, 108° or 72°
For the x - solving problems: x = 9, x = 5