In 3ABC, +A+ +B = 70c and +B + +C = 135c. Find the measure of each angle of the triangle.
Answers
Answer:
∠A=45°, ∠B = 25° and ∠C=110°
Step-by-step explanation:
In ΔABC
∠A+∠B=70°
∠B+∠C=135°
We need to find the each angle of triangle.
Add both equation and we get
∠A + ∠B + ∠B + ∠C = 70° + 135°
(∠A + ∠B + ∠C)+∠B = 205° (Angle sum property of triangle)
180° + ∠B = 205°
∠B = 205° - 180°
∠B = 25°
∠A+∠B=70°
∠A+25°=70°
∠A=45°
∠B + ∠C=135°
25° + ∠C=135°
∠C=110°
Hence, ∠A=45°, ∠B = 25° and ∠C=110° are angles of triangle.
"Given that triangle ABC
a+b = 70 ---------------(1),
b+c = 135 ---------------(2)
for every triangle sum of the angles = 180
a+b+c = 180
substitute a+b =70 in the above equation
we get 70 + c = 180
c = 180 – 70 = 110
substitute c = 110 in equation (2)
b + 110 =135
b = 135 – 110 = 25
substitute b = 25 in equation (1)
a + 25 = 70
a = 70 – 25 = 45
therefore, a = 45, b = 25, c = 110"