Question

Question 
ABC is a right triangle. AM is perpendicular to BC. The size of angle ABC is equal to 55 degrees. Find the size of angle MAC. [Refer to the attachment for diagram]

Note :-
\sf \implies \: Do \: not \: spam⟹Donotspam 
\sf \implies \: \: Do \: not \: copy⟹Donotcopy 

Spam = Id report​

Answer 1

Given:-

• ABC is a right-angled triangle at A
• AM is perpendicular to BC, i.e. AM ⊥ BC
• And ∠ABC = 55°

To find:-

• ∠MAC

In triangle ABC, we have,

• ∠ABC = 55°
• ∠BAC = 90°

By angle sum property if a triangle,

The sum of all three angles of a triangle is 180°.

• ⇒ ∠ABC + ∠BAC + ∠ACB = 180°
• ⇒ 55° + 90° + ∠ACB = 180°
• ⇒ 145° + ∠ACB = 180°
• ⇒ ∠ACB = 180° - 145°
• ⇒ ∠ACB = 35°

Now,

In triangle AMC, we have,

• ∠AMC = 90°
• ∠ACM = 35°

By angle sum property if a triangle,

The sum of all three angles of a triangle is 180°.

• ⇒ ∠AMC + ∠ACM + ∠MAC = 180°
• ⇒ 90° + 35° + ∠MAC = 180°
• ⇒ 125° + ∠MAC = 180°
• ⇒ ∠MAC = 180° - 125°
• ⇒ ∠MAC = 55°

Hence,

The value of ∠MAC is 55°