We want to find m∠ ABD and m∠ DBC given that m∠ ABC=95^(∘). The expression m∠ ABD indicates the measure of the angle between two rays, BA and BD. Similarly, the expression m∠ DBC indicates the measure of the angle between rays BD and BC. 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 have that m∠ ABC is equal to the sum of m∠ ABD and m∠ DBC. Therefore, we can create an equation using the expressions for the two smaller angles, m∠ ABD= (2x+23) and m∠ DBC= (9x-5), and the value of the larger angle, m∠ ABC = 95.
m∠ ABD+m∠ DBC=m∠ ABC
⇓
(2x+23)+ (9x-5)= 95
Now, we can solve this equation for x.
Having solved the equation, we can calculate the measures of individual angles by substituting x= 7 into the expressions for the unknown angles.
m∠ ABD:& 2( 7)+23=37^(∘)
m∠ DBC:& 9( 7)-5 =58^(∘)
The measure of angle ∠ ABD is 37^(∘) and the measure of ∠ DBC is 58^(∘).
