Question

find the measure of ∠ctg.

Explanation:

Step1: Identify angle - sum relationship

The measure of $\angle CTG$ is the sum of the two adjacent - angle measures given.
The two adjacent angles are $\angle CTG_1=x + 45$ and $\angle CTG_2=x + 20$.
So, $m\angle CTG=(x + 45)+(x + 20)$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms:
$(x + 45)+(x + 20)=x+x + 45+20=2x + 65$.

However, if we assume there is no $x$ value given and we just want to express the sum of the two angle - expressions in simplest form, the measure of $\angle CTG$ is $2x + 65$. If we assume this is a right - angled situation where the sum of the two non - right angles in a right - triangle formed by these rays is $90^{\circ}$ (not clear from the given diagram), we would set up an equation to solve for $x$ first. But without further information, the measure of $\angle CTG$ in terms of the given expressions is $2x + 65$.

Answer:

$2x + 65$