In Figure 3, if m∠BCE = 83° and m∠DEB = 26°, then find m∠LJK: 2. In Figure 4a, if m∠JKL = 78° and m∠MNL = 26°, find m∠L1: 3. In Figure 4b, if m∠R = 69° and m∠QR = 87°, then find m∠... In Figure 3, if m∠BCE = 83° and m∠DEB = 26°, then find m∠LJK: 2. In Figure 4a, if m∠JKL = 78° and m∠MNL = 26°, find m∠L1: 3. In Figure 4b, if m∠R = 69° and m∠QR = 87°, then find m∠L2: 4. In Figure 4c, if m∠BHI = 250° and m∠L1 = 19°, m∠JK = 56°, then find m∠M3: 5. In Figure 4d, if m∠M2 = ... Read more

Steps to Solve

1. Finding m∠LJK using m∠BCE and m∠DEB

Using the fact that angles formed by two secants intersecting outside of the circle have a relationship given by the formula:

$$ m∠LJK = m∠BCE - m∠DEB $$

Substituting the known values:

$$ m∠LJK = 83° - 26° = 57° $$

2. Finding m∠L1 using m∠JKL and m∠MNL

The angles formed by secants with a common vertex inside the circle can be calculated as:

$$ m∠L1 = m∠JKL - m∠MNL $$

Substituting the values:

$$ m∠L1 = 78° - 26° = 52° $$

3. Finding m∠L2 using m∠R and m∠QR

For angles where two secants intersect at a point that is inside the circle:

$$ m∠L2 = m∠QR - m∠R $$

Substituting known values:

$$ m∠L2 = 87° - 69° = 18° $$

4. Finding m∠M3 using m∠BHI, m∠L1, and m∠JK

The sum of the exterior angle and the two interior angles formed can be calculated as:

$$ m∠M3 = m∠BHI - m∠L1 - m∠JK $$

Substituting known values:

$$ m∠M3 = 250° - 19° - 56° = 175° $$

5. Finding m∠M2 from previous angles

If necessary, continue resolving any remaining expressions based on previously found angles or any additional relationships provided in the problem.