Question

find the measure of the given angle.
find ( mangle abc ) if ( mangle abd = 70^circ ) and ( mangle dbc = 43^circ ).

Explanation:

Step1: Identify angle addition

To find \( m\angle ABC \), we use the angle addition postulate, which states that if a point \( D \) lies in the interior of \( \angle ABC \), then \( m\angle ABC = m\angle ABD + m\angle DBC \).

Step2: Substitute given values

We know \( m\angle ABD = 70^\circ \) and \( m\angle DBC = 43^\circ \). Substitute these values into the formula:
\( m\angle ABC = 70^\circ + 43^\circ \).

Step3: Calculate the sum

Add the two angle measures: \( 70 + 43 = 113 \). So, \( m\angle ABC = 113^\circ \).

Answer:

\( 113^\circ \)