Given ΔDAC is a right-angled triangle with right angle at A. Find the measure of ∠C?
Give reasons.
Answers
Answer:
Consider ABC as a right-angled triangle with ∠C=90
∘
We know that the sum of all the angles in a triangle is 180
∘
.
So we can write it as
∠A+∠B+∠C=180
∘
We can write it as
∠A+∠B=180
∘
−∠C
By substituting the values
∠A+∠B=180
∘
−90
∘
By subtraction
∠A+∠B=90
∘
Let us consider ∠A=53
∘
By substituting the value of ∠A in ∠A+∠B=90
∘
We get
53
∘
+∠B=90
∘
On further calculation
∠B=90
∘
−53
∘
By subtraction
∠B=37
∘
Therefore, ∠A=53
∘
,∠37
∘
and ∠C=90
Step-by-step explanation:
Consider ABC as a right-angled triangle with ∠C=90
∘
We know that the sum of all the angles in a triangle is 180
∘
.
So we can write it as
∠A+∠B+∠C=180
∘
We can write it as
∠A+∠B=180
∘
−∠C
By substituting the values
∠A+∠B=180
∘
−90
∘
By subtraction
∠A+∠B=90
∘
Let us consider ∠A=53
∘
By substituting the value of ∠A in ∠A+∠B=90
∘
We get
53
∘
+∠B=90
∘
On further calculation
∠B=90
∘
−53
∘
By subtraction
∠B=37
∘
Therefore, ∠A=53
∘
,∠37
∘
and ∠C=90