Question

Plz help me.

Triangle JKL is equilateral. All three interior angles have equal measures.


What is the measure of exterior angle 1?
30 degrees
60 degrees
120 degrees
130 degrees

Answer 1

Answer: 60 degrees

Explanation: the angles of a triangle sum to 180 degrees, and all the angles in an equilateral triangle are the same so every angle in an equilateral triangle must equal 60 degrees.

Answer 2

`{\underline {\boxed {\Large {\bf \gray { {120}^(\circ) } }}}}`

Given :

• In ∆ JKL , all the three interior angles have equal measures.

To calculate:

• Measure of
`\angle` 1 ( Exterior angle )

Calculation:

Here, we can solve this question in two ways.

• By exterior angle property of ∆.
• By linear pair.

______________________________

Let us calculate the measure of interior angles first.

→ Let the measure of each interior angle be x.

As all the interior angles of the triangle are equal,

`\sf { \dashrightarrow {180}^(\circ) = {x}^(\circ) +{x}^(\circ)+{x}^(\circ) }`

[ By angle sum property of ∆ ]

`\sf { \dashrightarrow {180}^(\circ) = {3x}^(\circ) }`

`\sf { \dashrightarrow \frac{{180}^(\circ)}{3} = {x}^(\circ) }`

`\sf\red { \dashrightarrow {60}^(\circ) = {x}^(\circ) }`

Therefore, measure of each interior angle of the triangle is 60°.

By exterior angle property of ∆ :

As we know that,

• Sum of two opposite interior angles of ∆ = Exterior angle

`\sf { \dashrightarrow \angle 1 = \angle K + \angle L}`

`\sf { \dashrightarrow \angle 1 = {60}^(\circ) + {60}^(\circ) }`

`\sf \green { \dashrightarrow \angle 1 = {120}^(\circ) }`

⇒ Hence, measure of angle 1 is 120°.

By linear pair:

→
`\angle` 1 +
`\angle` J = 180°

→
`\angle` 1 + 60° = 180°

→
`\angle` 1 = 180° - 60°

→
`\angle` 1 = 120°

⇒ Hence, measure of angle 1 is 120°.