Question

in the figure below, m∠abd=87°, and m∠1 is 19° more than m∠2. find m∠2.

Explanation:

Step1: Define variables for angles

Let \( m\angle 2 = x \). Then \( m\angle 1 = x + 19^\circ \) (since \( m\angle 1 \) is \( 19^\circ \) more than \( m\angle 2 \)).

Step2: Use angle sum property

We know that \( m\angle ABD = m\angle 1 + m\angle 2 \) and \( m\angle ABD = 87^\circ \). So we can write the equation:
\( x + (x + 19^\circ) = 87^\circ \)
Simplify the left - hand side: \( 2x+19^\circ = 87^\circ \)

Step3: Solve for x

Subtract \( 19^\circ \) from both sides of the equation:
\( 2x=87^\circ - 19^\circ \)
\( 2x = 68^\circ \)
Divide both sides by 2:
\( x=\frac{68^\circ}{2}=34^\circ \)

Answer:

\( 34 \)