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Geometry question - Given: AB and AC are the legs of isosceles triangle ABC, measure of angle 1 = 5x, measure of angle three = 2x + 12. Find measure of angle 2 (reference picture)

Geometry Question Given AB And AC Are The Legs Of Isosceles Triangle ABC Measure Of Angle 1 5x Measure Of Angle Three 2x 12 Find Measure Of Angle 2 Reference Pi class=

Sagot :

Since triangle, ABC is an isosceles triangle because AB = BC

Then the angles of its base are equal

Since the angles of its bases are <2 and <4, then

[tex]m\angle2=m\angle4[/tex]

Since <3 and <4 are vertically opposite angles

Since the vertically opposite angles are equal in measures, then

[tex]m\angle3=m\angle4[/tex]

Since measure of <3 = 2x + 12, them

[tex]m\angle4=m\angle2=2x+12[/tex]

Since <1 and <2 are linear angles

Since the sum of the measures of the linear angles is 180 degrees, then

[tex]m\angle2+m\angle1=180[/tex]

Since m<1 = 5x, then

[tex]\begin{gathered} m\angle1=5x \\ m\angle2=2x+12 \\ 2x+12+5x=180 \end{gathered}[/tex]

Add the like terms on the left side

[tex]\begin{gathered} (2x+5x)+12=180 \\ 7x+12=180 \end{gathered}[/tex]

Subtract 12 from both sides

[tex]\begin{gathered} 7x+12-12=180-12 \\ 7x=168 \end{gathered}[/tex]

Divide both sides by 7

[tex]\begin{gathered} \frac{7x}{7}=\frac{168}{7} \\ x=24 \end{gathered}[/tex]

Then substitute x by 24 in the measure of <2

[tex]\begin{gathered} m\angle2=2x+12 \\ m\angle2=2(24)+12 \\ m\angle2=48+12 \\ m\angle2=\mathring{60} \end{gathered}[/tex]

The measure of angle 2 is 60 degrees

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