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100 POINTS!!!!!!!!!!!!!!1 PLEASE SOLVE THESE PROBLEMS QUICKLY WITH AN EXPLANATION

100 POINTS1 PLEASE SOLVE THESE PROBLEMS QUICKLY WITH AN EXPLANATION class=
100 POINTS1 PLEASE SOLVE THESE PROBLEMS QUICKLY WITH AN EXPLANATION class=

Sagot :

Tushargupta0691idn

In  triangle ABC, if m∠B = 90°, BH = AH, and the ratio of m∠A to m∠C is 1:2, then m∠BHA = 120° (C).

In the next given equilateral triangle ABC, y = 70°.

Finding m∠BHA:

In triangle ABC, it is given that,

∠B = 90°

And m∠A : m∠C = 1:2

Let us assume m∠A is x. Then, m∠C = 2x

According to the angle sum property of a triangle,

∠A + ∠B + ∠C = 180°

90° + x + 2x = 180°

90° + 3x = 180°

3x = 90°

x = 30°

⇒ In triangle ABC, ∠A = 30° and ∠C = 60°

Now, in triangle AHB, it is also given that,

BH = AH

⇒ ∠ABH = ∠A = 30°

Thus, according to the angle sum property of a triangle,

∠ABH + ∠A + ∠BHA = 180°

30° + 30° + ∠BHA = 180°

∠BHA = 180° - 60°

∠BHA = 120°

Finding y in the Second Triangle:

Since triangle ABC is equilateral,

∠A = ∠B = ∠C = 60°

∴ x + 2x + 3x = 60°

6x = 60°

x = 10°

In triangle ABD, using angle sum property of triangle,

x + ∠B +  ∠BDA = 180°

10° + 60° + ∠BDA = 180°

∠BDA = 180° - 70°

∠BDA = 110°

Now, since, ∠BDA and y are linearly adjacent  angles,

∠BDA + y = 180°

110° + y = 180°

y = 180° - 110°

y = 70°  

Learn more about a triangle here:

https://brainly.com/question/2773823

#SPJ1

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