Question

If LaTeX: m\angle ABJ=28^\circm ∠ A B J = 28 ∘, LaTeX: \angle ABC\cong\angle DBJ∠ A B C ≅ ∠ D B J, find LaTeX: Triangle JBC.

Answer 1

To find the measure of ∠JBC, we use the property that the sum of angles in a triangle is 180 degrees. Since ∠ABC is congruent to ∠DBJ, and given m∠ABJ = 28°, we establish that both ∠ABC and ∠DBJ measure 76°. Consequently, ∠JBC also measures 76°.

Step-by-step explanation:

To find the measure of the ∠JBC given that m∠ABJ = 28° and ∠ABC ≅ ∠DBJ, we use the concept that the sum of angles in a triangle is 180 degrees. Since ∠ABC and ∠DBJ are congruent, they have the same measure. First, let's find the measure of ∠ABC and subsequently the measure of ∠JBC within △JBC.

We already have one angle of the triangle, which is ∠ABJ = 28°. If we denote the measure of ∠ABC (which is the same as the measure of ∠DBJ) as x, and we denote the measure of ∠JBC as y, our equation based on the triangle angle sum property is:

28° + x + x = 180°

This simplifies to:

28° + 2x = 180°

Subtracting 28° from both sides gives:

2x = 152°

Dividing by 2, we find:

x = 76°

So, both ∠ABC and ∠DBJ measure 76°. Next, we use this information to find y:

28° + 76° + y = 180°

Add 28° and 76° to get 104°:

104° + y = 180°

Finally, subtract 104° from both sides to get:

y = 76°

Therefore, the measure of ∠JBC is also 76° in triangle JBC.