Question

q. if < abc = 103°, find m< abd

Explanation:

Step1: Set up equation based on angle - addition

Since $\angle ABC=\angle ABD+\angle DBC$, we have $(3x + 1)+(4x-3)=103$.

Step2: Combine like - terms

Combining the $x$ terms and the constant terms on the left - hand side gives $3x+4x+1 - 3=103$, which simplifies to $7x-2 = 103$.

Step3: Solve for $x$

Add 2 to both sides of the equation: $7x-2 + 2=103 + 2$, so $7x=105$. Then divide both sides by 7: $x=\frac{105}{7}=15$.

Step4: Find $\angle ABD$

Substitute $x = 15$ into the expression for $\angle ABD$ which is $3x + 1$. So $\angle ABD=3\times15+1=45 + 1=46^{\circ}$.

Answer:

$46^{\circ}$