Question

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)

Answer 1

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

`m\angle2=m\angle4`

Since <3 and <4 are vertically opposite angles

Since the vertically opposite angles are equal in measures, then

`m\angle3=m\angle4`

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

`m\angle4=m\angle2=2x+12`

Since <1 and <2 are linear angles

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

`m\angle2+m\angle1=180`

Since m<1 = 5x, then

`\begin{gathered} m\angle1=5x \\ m\angle2=2x+12 \\ 2x+12+5x=180 \end{gathered}`

Add the like terms on the left side

`\begin{gathered} (2x+5x)+12=180 \\ 7x+12=180 \end{gathered}`

Subtract 12 from both sides

`\begin{gathered} 7x+12-12=180-12 \\ 7x=168 \end{gathered}`

Divide both sides by 7

`\begin{gathered} (7x)/(7)=(168)/(7) \\ x=24 \end{gathered}`

Then substitute x by 24 in the measure of <2

`\begin{gathered} m\angle2=2x+12 \\ m\angle2=2(24)+12 \\ m\angle2=48+12 \\ m\angle2=\mathring{60} \end{gathered}`

The measure of angle 2 is 60 degrees