Question

Plz help me.

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 ∆ ]

$\sf { \dashrightarrow {180}^{\circ} = {3x}^{\circ} }$

$\sf { \dashrightarrow \dfrac{{180}^{\circ}}{3} = {x}^{\circ} }$

$\sf\red { \dashrightarrow {60}^{\circ} = {x}^{\circ} }$

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°.