Question

in the diagram below we have that $d\widehat{u}v = 73^{circ}$ and $c\widehat{b}t = 61^{circ}$. find: 1. $c\widehat{t}b =$ 2. $a\widehat{b}t =$ 3. $t\widehat{u}c =$

Explanation:

Step1: Recall linear - pair property

Since $\angle CBT = 61^{\circ}$ and $\angle ABT$ and $\angle CBT$ form a linear - pair (a straight - line angle which is $180^{\circ}$), we use the formula $\angle ABT=180^{\circ}-\angle CBT$.
$\angle ABT = 180 - 61=119^{\circ}$

Step2: Use corresponding - angles property

Given $\angle DUV = 73^{\circ}$, and $\angle TUC$ and $\angle DUV$ are corresponding angles (assuming parallel lines and transversals in the diagram), so $\angle TUC=\angle DUV = 73^{\circ}$. Also, $\angle CTB=\angle CBT = 61^{\circ}$ because of the given equal - angle notation in the problem (it seems to imply some isosceles - like or equal - angle relationship in the context of the diagram).

Answer:

1. $61$
2. $119$
3. $73$