Question

enter the given angle measure into the diagram.
given:

• ( eb perp jd ).
• ( mangle qed = 130^circ ).

enter each measure required to calculate ( mangle beq ), starting with the given information.

• the measure of ( angle beq ) can be calculated.

( mangle beq = square^circ )

• the measure of ( angle beq ) can not be calculated.

diagram notes:
diagram shows lines with point e, and lines jd, eb, eq. d and j are on a vertical line, b is on a horizontal line, q is on a line from e making an angle with ed.

Explanation:

Step1: Identify right angle

Since \( EB \perp JD \), \( \angle BED = 90^\circ \) (definition of perpendicular lines).

Step2: Use angle subtraction

We know \( m\angle QED = 130^\circ \) and \( \angle BED = 90^\circ \). Let \( m\angle BEQ = x \). Then \( x + 90^\circ = 130^\circ \) (angle addition postulate for \( \angle QED \) as the sum of \( \angle BEQ \) and \( \angle BED \)).

Step3: Solve for \( x \)

Subtract \( 90^\circ \) from both sides: \( x = 130^\circ - 90^\circ = 40^\circ \).

Answer:

\( 40 \)