Question

If 3 angles A, B and C of △ABC are in a ratio of 7 : 5 : 3, what is the measure of ∠A ?

Answer 1

Given:  $3$ angles A, B and C of △ABC are in a ratio of $7 : 5 : 3$.

To Find: The measure of ∠A.

Solution:

• We know that Angle Sum Property of a triangle states that:

∠A + ∠B + ∠C = 180°

1. Let ∠A = 7x
2. Let ∠B = 5x
3. Let ∠C = 3x

• So, we can conclude that:

$7x + 5x + 3x = 180$° (Since ∠A + ∠B + ∠C = 180°)

• Add accordingly:

$15x = 180$°

• Take 15 to the other side and hence, convert the operation in Divide.

$x = \frac{180}{15}$

• Divide accordingly:

$x$ = $12$°

• Now, find all angles:

1. ∠A = 7x

        ∠A $= 7$ × $12$ °

        ∠A $= 84$°

Final Answer:

Hence, the measure of angle A is $84$°.