Question

1. find x and m∠abd

a
(4x + 3)°
d
b
39°
c
x = ___
m∠abd = ___

Explanation:

Step1: Identify the right angle

Since \( \angle ABC \) is a right angle (marked with the square), it measures \( 90^\circ \). So, \( \angle ABD + \angle DBC = 90^\circ \).

Step2: Set up the equation

We know \( \angle ABD = (4x + 3)^\circ \) and \( \angle DBC = 39^\circ \). So, \( (4x + 3) + 39 = 90 \).

Step3: Solve for x

Simplify the left side: \( 4x + 42 = 90 \). Subtract 42 from both sides: \( 4x = 90 - 42 = 48 \). Divide by 4: \( x = \frac{48}{4} = 12 \).

Step4: Find \( m\angle ABD \)

Substitute \( x = 12 \) into \( 4x + 3 \): \( 4(12) + 3 = 48 + 3 = 51 \).

Answer:

\( x = 12 \)
\( m\angle ABD = 51^\circ \)