Question

given: ∠1 = 90° ∠2 = 34° ∠6 = 137° 13. < 3 = 90° 14. < 8 = 15. < 4 =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles. Given $\angle1 = 90^{\circ}$, so $\angle3=90^{\circ}$.

Step2: Use linear - pair property

$\angle6$ and $\angle8$ are a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. Given $\angle6 = 137^{\circ}$, then $\angle8=180^{\circ}-\angle6=180 - 137=43^{\circ}$.

Step3: Use angle - sum property of a triangle - like configuration

$\angle2$, $\angle4$ and the angle adjacent to $\angle3$ (which is $90^{\circ}$) form a straight - line (or can be considered in a linear - pair or angle - sum context). The sum of angles on a straight - line is $180^{\circ}$. Given $\angle2 = 34^{\circ}$ and the adjacent angle to $\angle3$ is $90^{\circ}$, then $\angle4=180-(90 + 34)=56^{\circ}$.

Answer:

1. $90$
2. $43$
3. $56$