Question

One of the exterior angles of a triangle is 120 degree and it's interior opposite angles are in the ratio 1:5. Find the adjacent angle.
(a) 160 degree
(b) 60 degree
(c) 34 degree
(d) 180 degree

Answer 1

Hello, Buddy!!

Refer The Attachment ⤴️

Let, The required angle be z

• Exterior Angle = Sum of two opposite interior angles.

Then, (1x+5x) = 120°

But, 1x+5x+z = 180° [Sum of Interior Angles of a Triangle]

→ 120°+z= 180°

→ z = 180°-120°

→ z = 60°

• Required Angle ➪ 60°

_____________________________

WKT

Adjacent Angles are Supplementary.

→ z+120° = 180°

→ z = 180°-120°

→ z = 60°

• Required Angle ➪ 60°

@MrMonarque♡

Hope It Helps You ✌️

Answer 2

Answer:

$60^{0}$

Step-by-step explanation:

Given data:

• One of the exterior angle of a triangle is $120^{0}$ and its interior opposite angles are in the ratio $1:5$

• As we know that sum of interior angles of a triangle $=180^{0}$

• The exterior angle of a triangle is equal to the sum of the opposite interior angles

• Let the opposite interior angles be $x,5x$

• According to the given data

$x+5x=120^{0}$

$6x=120^{0}$

$x=20^{0}$

• The opposite interior angles are $20^{0}$, $5x=5(20^{0} )$$=100^{0}$

• Adjacent angle $=180-20-100=180-120=60^{0}$

Hence, the measure of the adjacent angle is $60^{0}$.