![{\underline {\boxed {\Large {\bf \gray { {120}^{\circ} } }}}}](https://tex.z-dn.net/?f=%20%7B%5Cunderline%20%7B%5Cboxed%20%7B%5CLarge%20%7B%5Cbf%20%5Cgray%20%7B%20%7B120%7D%5E%7B%5Ccirc%7D%20%7D%20%7D%7D%7D%7D%20)
<u>Given</u> :
• In ∆ JKL , all the three interior angles have equal measures.
<h2><u>To calculate</u>:</h2>
• Measure of
1 ( Exterior angle )
<h2><u>Calculation</u>:</h2>
Here, we can solve this question in two ways.
- By exterior angle property of ∆.
- By linear pair.
______________________________
<u>Let us calculate the measure of interior angles first</u>.
→ 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} }](https://tex.z-dn.net/?f=%20%5Csf%20%7B%20%5Cdashrightarrow%20%7B180%7D%5E%7B%5Ccirc%7D%20%3D%20%7Bx%7D%5E%7B%5Ccirc%7D%20%2B%7Bx%7D%5E%7B%5Ccirc%7D%2B%7Bx%7D%5E%7B%5Ccirc%7D%20%7D%20)
[ By angle sum property of ∆ ]
![\sf { \dashrightarrow {180}^{\circ} = {3x}^{\circ} }](https://tex.z-dn.net/?f=%20%5Csf%20%7B%20%5Cdashrightarrow%20%7B180%7D%5E%7B%5Ccirc%7D%20%3D%20%7B3x%7D%5E%7B%5Ccirc%7D%20%7D%20)
![\sf { \dashrightarrow \dfrac{{180}^{\circ}}{3} = {x}^{\circ} }](https://tex.z-dn.net/?f=%20%5Csf%20%7B%20%5Cdashrightarrow%20%5Cdfrac%7B%7B180%7D%5E%7B%5Ccirc%7D%7D%7B3%7D%20%3D%20%7Bx%7D%5E%7B%5Ccirc%7D%20%7D%20)
![\sf\red { \dashrightarrow {60}^{\circ} = {x}^{\circ} }](https://tex.z-dn.net/?f=%20%5Csf%5Cred%20%7B%20%5Cdashrightarrow%20%20%7B60%7D%5E%7B%5Ccirc%7D%20%20%3D%20%7Bx%7D%5E%7B%5Ccirc%7D%20%7D%20)
Therefore, measure of each interior angle of the triangle is 60°.
<h3><u>By exterior angle property of ∆ </u>:</h3>
As we know that,
- Sum of two opposite interior angles of ∆ = Exterior angle
![\sf { \dashrightarrow \angle 1 = \angle K + \angle L}](https://tex.z-dn.net/?f=%20%5Csf%20%7B%20%5Cdashrightarrow%20%5Cangle%201%20%3D%20%5Cangle%20K%20%2B%20%5Cangle%20L%7D%20)
![\sf { \dashrightarrow \angle 1 = {60}^{\circ} + {60}^{\circ} }](https://tex.z-dn.net/?f=%20%5Csf%20%7B%20%5Cdashrightarrow%20%5Cangle%201%20%3D%20%7B60%7D%5E%7B%5Ccirc%7D%20%2B%20%20%7B60%7D%5E%7B%5Ccirc%7D%20%20%7D%20)
![\sf \green { \dashrightarrow \angle 1 = {120}^{\circ} }](https://tex.z-dn.net/?f=%20%5Csf%20%5Cgreen%20%7B%20%5Cdashrightarrow%20%5Cangle%201%20%3D%20%7B120%7D%5E%7B%5Ccirc%7D%20%20%7D%20)
⇒ Hence, measure of angle 1 is 120°.
<h3><u>By linear pair</u>:</h3>
→
1 +
J = 180°
→
1 + 60° = 180°
→
1 = 180° - 60°
→
1 = 120°
⇒ Hence, measure of angle 1 is 120°.