Number 1
[tex]\begin{gathered} M\measuredangle DBA+M\measuredangle ABE=90^0\text{ (false bec}ause90^{0\text{ }}+90^0=180^0) \\ \end{gathered}[/tex]
Number 2
[tex]\begin{gathered} _{\measuredangle\text{ DBC }+\measuredangle DBT\text{ }\ne90^0} \\ False\text{ is not complementary because }_{\measuredangle\text{ DBC }+\measuredangle DBCisgreaaterthan90^0} \\ \measuredangle DBC=90 \\ \measuredangle DBT=30^0 \\ FT\text{ is a straight line } \\ 60+90+\measuredangle DBT=180\text{ (sum of angles on a striaght line)} \\ \measuredangle DBT=180-150 \\ \measuredangle DBT=30^0 \end{gathered}[/tex]
Recall, Complementary angles are two angles whose sum up to 90degrees
Number 3
[tex]\begin{gathered} \measuredangle ABE=90^0\text{ and M}\measuredangle ABF=60^0 \\ M\measuredangle FBE+M\measuredangle ABF=90^0 \\ M\measuredangle FBE+60=90 \\ M\measuredangle FBE\text{ =90-60} \\ M\measuredangle FBE=30^0 \\ It\text{ is true } \end{gathered}[/tex]
Number 4
[tex]\begin{gathered} M\measuredangle\text{DBC}+M\measuredangle CBE=180^0(\text{supplementary angles)} \\ \text{false if you say it is not supplementary} \\ \text{because }M\measuredangle\text{DBC}+M\measuredangle CBE=180^0 \end{gathered}[/tex]
Recall, supplementary angles are two angles whose sum up to 180degrees
Number 5
[tex]A,\text{ B , C are collinear because A, B, C are on a straight line}[/tex]
Number 6
[tex]\begin{gathered} \measuredangle FBE=\measuredangle DBT\text{ }=30^0 \\ It\text{ is true because Vertically opposite angles are equal} \end{gathered}[/tex]
Number 7
[tex]\begin{gathered} m\measuredangle ABF\text{ }+m\measuredangle FBE\text{ }\ne m\measuredangle ABE \\ \text{false because }m\measuredangle ABF\text{ }+m\measuredangle FBE\text{ =}m\measuredangle ABE\text{ (supplementary } \\ \text{angles)} \end{gathered}[/tex]
Number 8
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