Question

angle ACD is an exterior angle of ∆ABC, angleB=45• and angleA=65•. find the measure of angle ACD​

Answer 1

Given:-

• $\sf{\angle ACD}$ is an exterior angle of ∆ABC
• $\sf{\angle B = 45^\circ}$
• $\sf{\angle A = 65^\circ}$

To find:-

Measure of $\sf{\angle ACD}$

Note:-

Refer to the attachment for the diagram of the Question.

Solution:-

In ∆ABC,

$\sf{\angle CAB = 65^\circ}$

$\sf{\angle ABC = 45^\circ}$

According to the angle sum-property of a triangle,

$\sf{\angle CAB + \angle ABC + \angle BCA = 180^\circ}$

= $\sf{65^\circ + 45^\circ + \angle BCA = 180^\circ}$

= $\sf{110^\circ + \angle BCA = 180^\circ}$

= $\sf{\angle BCA = 180^\circ - 110^\circ}$

= $\sf{\angle BCA = 70^\circ}$

Therefore,

The measure of ∠BCA is 70°.

Now,

$\sf{\angle BCA + \angle ACD = 180^\circ\:\:\:[Linear\:Pair]}$

= $\sf{70^\circ + \angle ACD = 180^\circ}$

= $\sf{\angle ACD = 180^\circ - 70^\circ}$

= $\sf{\angle ACD = 110^\circ}$

Therefore the measure of ∠ACD is 110°.

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Additional Information:-

$\longrightarrow$ What is angle-sum property of a triangle?

✓ The angle-sum property of a triangle states that the sum of all sides of a triangle is always 180°

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✓ Try to draw a diagram for these kind of questions in order to make the question more easy to solve.

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Answer 2

✯ Given ✯

• ∠ACD is an exterior angle of ∆ABC.
• ∠B = 45°
• ∠A = 65°

✯ To find ✯

• ∠ACD = ?

꧁ Solution ꧂

We know that An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

So, according to the question:-

${\bf{\large{\longmapsto{ \: ∠ \: ACD = ∠A +∠B}}}}$

${\bf{\large{\longmapsto{ \: ∠ \: ACD =45 ° + 65 °}}}}$

${\large{ \underline{ \boxed{ \bf{ \red{\implies{ \: ∠ \: ACD =110 °}}}}}}}$

So, measure of angle ACD is 110°.