The expression m∠ABX indicates the measure of the angle between two rays, BA and BX. Similarly, the expression m∠CBX indicates the measure of the angle between rays BC and BX. To find their measures, let's start by identifying the three angles on a diagram.
Looking at the figures, and by the Angle Addition Postulate, we can see that m∠ABC is equal to the sum of m∠ABX and m∠CBX. We can solve for x by creating an equation using the expressions for the two smaller angles and the value of the larger angle. Note that ∠ABC is a straight angle, which is always equal to 180^(∘).
Having solved the equation, we can calculate the individual angles by substituting x= 3 into the expressions for the unknown angles.
m∠ABX &: 14( 3)+70=112^(∘)
m∠CBX &: 20( 3)+8 =68^(∘)
