Question

Find the measure of angle ABD from given figure.
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Answer 1

Answer:

120°

Step-by-step explanation:

Theorem:- exterior angle is equal to the sum of opposite 2 interior angles.

<ABD=70+50

=120°

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Answer 2

Answer: ∠ABD measures 120°.

Step-by-step explanation:

Concept: The angle sum property of a triangle states that the sum of all the interior angles of a triangle equals to 180º. A triangle is a polygon having three sides and three angles, one at each vertex. No matter whether a triangle is an acute angled, obtuse angled, or a right angled triangle, the sum of its interior angles always remains 180º.

Exterior angle property: when a side of a closed polygon is extended, then the line contains two adjacent angles, namely the interior angle and the exterior angle. The interior angle is present inside the polygon whereas the exterior angle is present outside the polygon on that side adjacent to the interior angle.

The straight line forms an angle of 180°, so,

exterior angle+interior angle = 180°.

Step 1: In the given triangle, ΔABC, it is given that,

∠BCA=50°, ∠CAB = 70°.

Now by applying the angle sum property of the traingle, we have,

∠ABC + ∠BAC + ∠ACB = 180°

⇒ ∠ABC + 70° + 50° = 180°

⇒∠ABC=180° - (70° + 50°) = 180° - 120° = 60°

Step 2: Here ∠ABD is the exterior angle adjacent to the interior angle ∠ABC on the side BC which is extended up to D.

So, from the exterior angle property, we get.

∠ABD+∠ABC= 180°

⇒∠ABD= 180° - ∠ABC = 180° - 60°= 120°

Final answer: The measure of the angle ∠ABD is 120°