Question

In a triangle one of the exterior angle is 105°. One of the interior opposite angle is 75°.
Find the measure of all the angles of the triangle.
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Answer 1

Answer:

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Step-by-step explanation:

let the two remaining interior angles of triangle be x and y

so now according to exterior angle property of triangle

exterior angle of a triangle=sum of its two opposite remote interior angles

so 105=75+x

so x=30

now by angle sum property of triangle

we get x+y+75=180

ie y+30+75=180

ie y=180-105

so y=75

hence the triangle has 75-75-30 degree as three angles in it

Answer 2

${ \huge{ \underline{ \boxed{ \mathcal{ \purple{Given}}}}}}$

• In a triangle one of the exterior angle is 105°. One of the interior opposite angle is 75°. Find the measure of all the angles of the triangle.

$\sf \huge \underline \purple{To \: Find}$

• The measure of all the angles of the triangle.

$\huge \mathfrak {\underline \purple{Solution}}$

Exterior angle = 105°

Interior opposite angle = ∠ABC = 75°

∠A = ∠ACX – LB

= 105° – 75°

= 30°

∠C = 180° – ∠ACX

= 180° – 105°

= 75°

[ ∠ACB and ∠ACX are supplementary angels ]