Question

find the measure of ∠abc

Explanation:

Step1: Find ∠ACB

Since ∠ACD and ∠ACB are supplementary (they form a linear pair), we know that $\angle ACB + 145^\circ = 180^\circ$. So, $\angle ACB = 180^\circ - 145^\circ = 35^\circ$.

Step2: Use triangle angle sum

In triangle ABC, the sum of angles is $180^\circ$. So, $95^\circ + 2x^\circ + 35^\circ = 180^\circ$. Combine like terms: $130^\circ + 2x^\circ = 180^\circ$. Subtract $130^\circ$: $2x^\circ = 50^\circ$. Thus, $\angle ABC = 2x^\circ = 50^\circ$.

Answer:

$50^\circ$