Question

If the measure of angle 6 is 45º, find the measure of the remaining angles.

Answer 1

Angle 1: 135

Angle 2: 45 (corresponding or same-side exterior to angle 6)

Angle 3: 135

Angle 4: 45 (alternate interior to 6)

Angle 5: 135

Angle 7: 135

Angle 8: 45 (vertical angle to 6)

Explanation:

Figure out which angles would be congruent to 6, then fill in the rest of them with 180-45, which equals 135.

Answer 2

∠ 1 = 135°

∠ 2 = 45°

∠ 3 = 135°

∠ 4 = 45°

∠ 5 = 135°

∠ 6 = 45°

∠ 7 = 135°

∠ 8 = 45°

Explanation:

Given:

• ∠ 6 = 45°

To find;

• All other angles:

Solution:

Since vertically opposite angles are equal.

So, ∠ 6 = ∠ 8 = 45°

Linear pair angles are supplementary.

So,

∠ 6 + ∠ 7 = 180°

Substitute the value of ∠ 6 and solve for ∠ 7 .

45° + ∠ 7 = 180°

∠ 7 = 180° - 45°

∠ 7 = 135°

Again,

vertically opposite angles are equal.

So, ∠ 7 = ∠ 5 = 135°

Now,

Corresponding angles are equal.

So,

∠ 6 = ∠ 2 = 45°

∠ 8 = ∠ 4 = 45°

∠ 5 = ∠ 1 = 135°

∠ 7 = ∠ 3 = 135°

So,

Final answer is:

• ∠ 1 = 135°
• ∠ 2 = 45°
• ∠ 3 = 135°
• ∠ 4 = 45°
• ∠ 5 = 135°
• ∠ 6 = 45°
• ∠ 7 = 135°
• ∠ 8 = 45°

`\hrulefill`

Note:

Vertically opposite angles are angles that are formed opposite each other when two lines intersect. They are always equal in measure.

Linear pair is a pair of adjacent angles that form a straight line. The sum of the measures of a linear pair is always 180 degrees.

Corresponding angles are angles that are located in the same relative position on two parallel lines when a transversal intersects them. Corresponding angles are always equal in measure.