Question

9.If an exterior angle of a triangle is 130⁰and one of the interior opposite angles is 60⁰, find the measures of the remaining angles of the triangle​

Answer 1

Answer:

ur answer 45 degrees

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Answer 2

Step-by-step explanation:

$Using the theorem that if the side of a triangle is produced then the interior angle is equal to the sum of two interior opposite angles of the triangle.</p><p></p><p>Let ΔABC be a triangle where the side BC is produced.</p><p></p><p>By the theorem we have</p><p></p><p>∠A+∠B=100o …………..(1)</p><p></p><p>It is given that the interior opposite angles are equal i.e., ∠A=∠B.</p><p></p><p>∴ Equation (1) becomes</p><p></p><p>2∠A=100o</p><p></p><p>⇒∠A=50o</p><p></p><p>⇒∠B=50o</p><p></p><p>Using angle sum property of a triangle,</p><p></p><p>Sum of all angles of a triangle =180o</p><p></p><p>⇒∠A+∠B+∠C=180o</p><p></p><p>⇒100+∠C=180o [from (1)]</p><p></p><p>⇒∠C=180o−100o</p><p></p><p>⇒∠C=80o.</p><p></p><p>Hence ∠A=50o</p><p></p><p>∠B=50o</p><p></p><p>∠C=80o.</p><p></p><p>Answer By</p><p></p><p>gentryamanshrma$

Using the theorem that if the side of a triangle is produced then the interior angle is equal to the sum of two interior opposite angles of the triangle.

Let ΔABC be a triangle where the side BC is produced.

By the theorem we have

∠A+∠B=100

o

…………..(1)

It is given that the interior opposite angles are equal i.e., ∠A=∠B.

∴ Equation (1) becomes

2∠A=100

o

⇒∠A=50

o

⇒∠B=50

o

Using angle sum property of a triangle,

Sum of all angles of a triangle =180

o

⇒∠A+∠B+∠C=180

o

⇒100+∠C=180

o

[from (1)]

⇒∠C=180

o

−100

o

⇒∠C=80

o

.

Hence ∠A=50

o

∠B=50

o

∠C=80

o

.

Answer By