Answer:
3. below
<D = 75°
<E = 37°
<F = 68°
4. below
<G = 50°
<H = 80°
<I = 50°
5. below
<A = 55°
<B = 90°
<C = 35°
Step-by-step explanation:
In a triangle, all angles add up to 180°, so we can set up equation accordingly:
3. m<E + m<F + m<D = 180°
6x + 1 + 68 + 13x - 3 = 180
19x + 66 = 180
19x = 114
x = 6°
We can substitute the value of x back into the expressions for each angle:
m<E = 6x + 1 = 6(6) +1 = 36 + 1 = 37°
m<F = 68°
m<D = 13x - 3 = 13(6) - 3 = 75°
4. m<G + m<I + m<H = 180°
2x + 2x + 4x - 20 = 180
8x - 20 = 180
8x = 200
x = 25°
We can substitute the value of x back into the expressions for each angle:
<G = 2x = 50°
<H = 4x - 20 = 4(25) - 20 = 80°
<I = 2x = 50°
5. m<B + m<C + m<A = 180°
90 + 3x + 5 + 5x + 5 = 180
100 + 8x = 180
8x = 80
x = 10°
We can substitute the value of x back into the expressions for each angle:
<A = 5x + 5 = 5(10) + 5 = 55°
<B = 90°
<C = 3x + 5 = 3(10) + 5 = 35°
