Math, asked by at3395136, 4 days ago

= In fig AB = AC and AP I BC and B = 60°. Then find (i) BAP (ii) ACB. A. B P С​

Answers

Answered by Anonymous
1

 \huge \mathfrak{\red{\underline{\underline{Solution:}}}}

Here, we are given with triangle ABC and some of the necessary conditions and measures of the angles:

  • AB = AC
  • AP ⟂ BC
  • Angle B = 60°

We have to find angle BAP and angle ACB

Finding angle BAP:

In triangle ∆APB,

  • Angle APB = 90°
  • Angle ABP = 60° (Angle B = 60° )

And we know that, the angle sum property of a triangle says that all angles of a triangle add upto 180°. So,

 \sf{ \longrightarrow{ \angle APB + \angle ABP + \angle BAP = 180 \degree}}

Substituting the values of given angles,

 \sf{ \longrightarrow{90 \degree + 60 \degree + \angle BAP = 180 \degree}}

 \sf{ \longrightarrow{ 150 \degree + \angle BAP = 180 \degree}}

 \sf{ \longrightarrow{ \boxed{ \red{ \sf{ \angle BAP = 30 \degree}}}}}

Hence, measure of angle BAP = 30°

Finding angle ACB:

In triangle ∆ABC,

  • AB = AC

We know that, equal angles faces equal sides in a triangle, so we can write that:

 \sf{ \longrightarrow{ \angle ABC = \angle ACB}}

 \sf{ \longrightarrow{60 \degree = \angle ACB}}

Flipping it,

 \sf{ \longrightarrow{ \boxed{ \sf{ \red{ \angle ACB = 60 \degree}}}}}

Hence, angle ACB = 60°

 \sf{\underline{\underline{Final \: Answers:}}}

  •  \sf{ \angle BAP = 30 \degree}

  •  \sf{ \angle ACB = 60 \degree}
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