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Line DA bisects angle EAC, line AB is congruent to line BC, measure of angle B is 74 and measure of angle EAD =44 degrees. Find measure of angle EAB.

Line DA Bisects Angle EAC Line AB Is Congruent To Line BC Measure Of Angle B Is 74 And Measure Of Angle EAD 44 Degrees Find Measure Of Angle EAB class=

Sagot :

From the given information, since AB is congruent to BC then triangle ABC is issoceles,

therefore, the base angles measure the same and they are denoted by x. Since interior angles of any triangle add up to 180, we have

[tex]74+x+x=180[/tex]

which gives

[tex]\begin{gathered} 74+2x=180 \\ 2x=180-74 \\ 2x=106 \\ x=\frac{106}{2} \\ x=53 \end{gathered}[/tex]

Then, each base angle measure 53 degrees.

On the other hand, since DA bisects angleEAC then angle DAC measure the same as angle EAD, that is,

Therefore, angleEAB is equal to

[tex]m\angle EAB=x+44+44[/tex]

By substituting our last result, we have

[tex]\begin{gathered} m\angle EAB=53+44+44 \\ m\angle EAB=53+88 \\ m\angle EAB=141 \end{gathered}[/tex]

then, the answer is 141 degrees

View image JennavieveY130355
View image JennavieveY130355
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