Question

In right ∆ABC, mLB - 90° and the difference.
between the measurments of LA and LC is 10°
Find the measurmeants of LA and LC​

Answer 1

☯ ∠A = 50° & ∠C = 40°

By the given information ,

• ∠A - 10° = ∠C

Now , using angle sum property of triangle ,

• Angle sum property of a triangle :- Sum of all angles of a triangle is always equal to 180° .

⇒ ∠A + ∠B + ∠C = 180°

⇒ ∠A + ∠A - 10° + 90° = 180°

⇒ 2∠A = 180° - 80°

⇒ ∠A = 100°/2

⇒ ∠A = 50°

Now , ∠C = ∠A - 10° = 50° - 10° → 40°

♦ ∠C = 40°

Hence ,

• ∠A = 50°
• ∠C = 40°

Answer 2

To Find:-

• Find the measurements.

Solution:-

Given,

∠A - 10° = ∠B

∠C = 90°

As we know that:-

Let ∠A be " x "

$\tt\implies \: \angle A \: + \: \angle B \: + \: \angle C = {180}^{\circ}$

$\tt\implies \: x + x - 10 + 90 = 180$

$\tt\implies \: 2x - 80 = 180$

$\tt\implies \: 2x = 180 - 80$

$\tt\implies \: 2x = 100$

$\tt\implies \: x = \cancel\dfrac{100} {2}$

$\tt\implies \: x = {50} ^ {\circ }$

Hence,

• $\tt \: \angle A = {50} ^ {\circ }$
• $\tt \: \angle B = 50 - 10 = {40} ^ {\circ }$
• $\tt \: \angle C = {90} ^ {\circ }$