Question

question
given ( m parallel n ), find the value of ( x ).
(there is a diagram with two parallel lines ( m ) and ( n ), and a transversal ( t ). the angle on line ( m ) is ( (2x - 20)^circ ), and the angle on line ( n ) is ( (3x + 10)^circ ))
answer attempt 1 out of 2
( x = ) input box submit answer

Explanation:

Step1: Identify angle relationship

The angles $(2x-20)^\circ$ and $(3x+10)^\circ$ are consecutive interior angles (same-side interior angles) formed by transversal $t$ intersecting parallel lines $m$ and $n$, so they are supplementary.

Step2: Set up equation

$2x - 20 + 3x + 10 = 180$

Step3: Simplify and solve for x

Combine like terms: $5x - 10 = 180$
Add 10 to both sides: $5x = 190$
Divide by 5: $x = 38$

Answer:

38