Question

1. if $overleftrightarrow{ab}perpoverleftrightarrow{cd}$, $mangle dce = 8x + 4$ and $mangle ecb=2x + 6$ find the measure of $angle ecb$. 19. find the measure of $angle dbc$. 20. find the measure of $angle abd$.

Explanation:

Step1: Use perpendicular - angle property for question 18

Since $\overline{AB}\perp\overline{CD}$, $\angle DCB = 90^{\circ}$. And $\angle DCE+\angle ECB=\angle DCB$. So, $(8x + 4)+(2x+6)=90$.

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Step2: Find measure of $\angle ECB$

Substitute $x = 8$ into the expression for $\angle ECB$. $\angle ECB=2x + 6=2\times8+6=16 + 6=22^{\circ}$

Step3: Use linear - angle property for question 19

Since $\angle ABC$ is a straight - angle ($180^{\circ}$), and $\angle ABC=\angle ABD+\angle DBC$. So, $(6x + 2)+(x + 3)=180$.

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Then $\angle DBC=x + 3=25+3=28^{\circ}$

Step4: Use linear - angle property for question 20

Since $\angle ABC$ is a straight - angle ($180^{\circ}$), and $\angle ABC=\angle ABD+\angle DBC$. So, $(4x + 2)+(2x+22)=180$.

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Then $\angle ABD=4x + 2=4\times26+2=104 + 2=106^{\circ}$

Answer:

1. $22^{\circ}$
2. $28^{\circ}$
3. $106^{\circ}$