Question

if m∠abd = 79°, what are m∠abc and m∠dbc?

Explanation:

To solve this, we assume \( \angle ABC \) is a straight angle (\( 180^\circ \)) and \( BD \) bisects it or there's a right angle context, but from the given \( m\angle ABD = 79^\circ \), if \( \angle ABC \) is supplementary or \( \angle DBC \) is complementary, but likely \( \angle ABC = 180^\circ - \angle DBC \) or if \( BD \) is an angle bisector, but more likely a right angle error. Wait, maybe \( \angle ABC \) is a straight angle, so \( m\angle ABC = 180^\circ \), and \( m\angle DBC = 180^\circ - 79^\circ = 101^\circ \)? No, that doesn't make sense. Wait, maybe \( \angle ABC \) is a right angle? No, the image shows squares, maybe right angles. Wait, the problem is likely that \( BD \) is a ray such that \( \angle ABD + \angle DBC=\angle ABC \), and if \( \angle ABC \) is a straight angle (\( 180^\circ \)), then \( m\angle DBC = 180^\circ - 79^\circ = 101^\circ \), but the squares suggest right angles? Wait, maybe the original problem has \( \angle ABC \) as a straight angle, so:

Step1: Assume \( \angle ABC \) is a straight angle (\( 180^\circ \))

\( m\angle ABC = 180^\circ \)

Step2: Use angle addition \( m\angle ABD + m\angle DBC = m\angle ABC \)

\( 79^\circ + m\angle DBC = 180^\circ \)

Step3: Solve for \( m\angle DBC \)

\( m\angle DBC = 180^\circ - 79^\circ = 101^\circ \)

But the squares (right angle symbols) suggest \( \angle ABC \) and \( \angle DBC \) are right angles? No, maybe a typo. Wait, maybe \( \angle ABD = 79^\circ \), and \( \angle ABC \) is a right angle? No, the image is unclear. Wait, the correct approach: if \( BD \) is a bisector or \( \angle ABC \) is a straight angle. Given the problem, likely \( m\angle ABC = 180^\circ \), \( m\angle DBC = 180 - 79 = 101^\circ \). But the squares (right angle boxes) suggest \( \angle ABC \) and \( \angle DBC \) are \( 90^\circ \)? No, that contradicts. Wait, maybe the problem is \( m\angle ABD = 79^\circ \), and \( \angle ABC \) is a straight angle, so \( m\angle ABC = 180^\circ \), \( m\angle DBC = 180 - 79 = 101^\circ \).

Answer:

\( m\angle ABC = 180^\circ \), \( m\angle DBC = 101^\circ \) (assuming \( \angle ABC \) is a straight angle). If there's a right angle, maybe error, but based on given, this is the solution.