Question

1. on a triangle, $\angle a$ is twice as large as $\angle b$, and $\angle c$ is $28^\circ$ less than $\angle b$. find the measure of all three angles.

$m\angle a = $
$m\angle b = $
$m\angle c = $

Explanation:

Step1: Define variables for angles

Let $m\angle B = x$. Then $m\angle A = 2x$, and $m\angle C = x - 28^\circ$.

Step2: Use triangle angle sum theorem

The sum of angles in a triangle is $180^\circ$, so:
$$2x + x + (x - 28^\circ) = 180^\circ$$

Step3: Simplify and solve for $x$

Combine like terms:
$$4x - 28^\circ = 180^\circ$$
Add $28^\circ$ to both sides:
$$4x = 208^\circ$$
Divide by 4:
$$x = 52^\circ$$

Step4: Calculate each angle

$m\angle A = 2x = 2\times52^\circ = 104^\circ$
$m\angle B = x = 52^\circ$
$m\angle C = x - 28^\circ = 52^\circ - 28^\circ = 24^\circ$

Answer:

$m\angle A = 104^\circ$
$m\angle B = 52^\circ$
$m\angle C = 24^\circ$