Question

1. find ( mangle abc ). diagram: horizontal line ( ebd ) with ( b ) as vertex, vertical ray ( ba ) (right angle at ( angle eba )), ray ( bc ) between ( ba ) and ( bd ). angles: ( angle abc = (5x + 3)^circ ), ( angle cbd = (3x + 7)^circ ). options: ( 53^circ ), ( 37^circ ), ( 10^circ ), ( 21^circ ).

Explanation:

Step1: Identify angle sum

Since \( \angle EBA \) is a right angle (\( 90^\circ \)) and \( \angle EBD \) is a straight angle (\( 180^\circ \)), the sum of \( (5x + 3)^\circ \), \( (3x + 7)^\circ \), and \( 90^\circ \) is \( 180^\circ \). So, \( (5x + 3)+(3x + 7)+90 = 180 \).

Step2: Solve for \( x \)

Simplify the equation: \( 8x + 10 + 90 = 180 \) → \( 8x + 100 = 180 \) → \( 8x = 80 \) → \( x = 10 \).

Step3: Find \( m\angle ABC \)

Substitute \( x = 10 \) into \( 5x + 3 \): \( 5(10)+3 = 53 \).

Answer:

\( 53^\circ \)