Question

name: kacsa using the diagram, identify a pair of angles for each relationship: a) vertical angles b) supplementary angles c) complementary angles d) adjacent angles

Explanation:

Step1: Recall vertical - angles definition

Vertical angles are opposite angles formed by two intersecting lines. In the diagram, $\angle EGF$ and $\angle BGC$ are vertical angles.

Step2: Recall supplementary - angles definition

Supplementary angles are two angles whose sum is $180^{\circ}$. $\angle EGF$ and $\angle FGB$ are supplementary since they form a straight - line and $35^{\circ}+145^{\circ} = 180^{\circ}$.

Step3: Recall complementary - angles definition

Complementary angles are two angles whose sum is $90^{\circ}$. $\angle EGF$ and $\angle AGB$ are complementary as $\angle AGB = 90^{\circ}-35^{\circ}=55^{\circ}$ and $35^{\circ}+55^{\circ}=90^{\circ}$.

Step4: Recall adjacent - angles definition

Adjacent angles share a common vertex and a common side. $\angle EGF$ and $\angle EGA$ are adjacent angles as they share vertex $G$ and side $GF$.

Answer:

a) $\angle EGF$ and $\angle BGC$
b) $\angle EGF$ and $\angle FGB$
c) $\angle EGF$ and $\angle AGB$
d) $\angle EGF$ and $\angle EGA$