(Geometry) Explain how you can use a straightedge and a compass to construct an angle that is both congruent and adjacent to a g

Question

WINSTONCH

9 days ago

6

(Geometry) Explain how you can use a straightedge and a compass to construct an angle that is both congruent and adjacent to a g

iven angle.

Mathematics

2 answers:

Zina [9.1K] · Answer 1 · 2026-03-18T18:16:57+03:00

Answer:

To replicate an angle congruent and adjacent to angle ABC, place the compass at point B and draw an arc exceeding twice the angle size. This arc will intersect segments BA and BC, which we will denote as D and E. Adjust the compass from D to E and create another arc from point D that intersects the first arc at F. Now, use the straightedge to connect B to F, extending it to a new point G such that its length mirrors AB and BC. You’ll achieve angle ABG with B as its vertex that is both adjacent and congruent to ABC.

Svet_ta [9.5K] · Answer 2 · 2026-03-18T18:14:03+03:00

Utilize a straightedge to sketch two lines that run parallel to each other, and then draw a perpendicular line that intersects them. Subsequently, use a compass to gauge the angles, which should be both congruent and adjacent.

Create an arc across the sides of the angle, letting it meet the rays at points A and B. Extend the arc beyond B for a bit more distance.

Position the compass at point B, adjusting it to the length of AB. 

While still centered at B, draw an arc that intersects the first arc we made at a new point, which we will call C.

Consequently, you’ll have AB = BC.

Given that OA=OB=OC, the angles AOB and BOC will be congruent.