Question

topic
class:
main ideas/questions\tnotes/examples
triangle
angle sum
theorem\tthe sum of the measures of the angles of a triangle is 180°.
\t\t$m\angle a + m\angle b + m\angle c = 180$
exterior
angle
theorem\tan exterior angle is formed by extending any one side of the triangle.
\t\tan exterior is always equal to the sum
\t\tof the two non - adjacent interior angles.
\t\t$m\angle 1 = m\angle 2 + m\angle 3$
directions: find all missing angles.
1.
\t\t$m\angle 1 = \underline{119}$
2.
\t\t$m\angle 1 = \underline{128}$
3.
\t\t$m\angle 1 = \underline{25}$
4.
\t\t$m\angle 1 = \underline{127}$
\t\t$m\angle 2 = \underline{}$
\t\t$m\angle 3 = \underline{}$
5.
\t\t$m\angle 1 = \underline{133}$
\t\t$m\angle 2 = \underline{}$
\t\t$m\angle 3 = \underline{}$
6.
\t\t$m\angle 1 = \underline{}$
\t\t$m\angle 2 = \underline{}$
\t\t$m\angle 3 = \underline{}$

1. $\overline{bc}$ bisects $\angle acd$

\t\t$m\angle 1 = \underline{87}$
\t\t$m\angle 2 = \underline{45}$
\t\t$m\angle 3 = \underline{45}$
\t\t$m\angle 4 = \underline{52}$
© gina wilson (all things algebra®, llc), 2014 - 20

Explanation:

Ejercicio 4

Paso 1: Calcular $\angle 3$

$\angle 3 = 180^\circ - 84^\circ = 96^\circ$

Paso 2: Calcular $\angle 2$

$\angle 2 = 180^\circ - (96^\circ + 43^\circ) = 41^\circ$

Paso 3: Calcular $\angle 1$

$\angle 1 = 180^\circ - (66^\circ + 41^\circ) = 73^\circ$

Ejercicio 5

Paso 1: Calcular $\angle 1$

$\angle 1 = 90^\circ - 12^\circ = 78^\circ$

Paso 2: Calcular $\angle 2$

$\angle 2 = 180^\circ - (90^\circ + 43^\circ) = 47^\circ$

Paso 3: Calcular $\angle 3$

$\angle 3 = 180^\circ - (78^\circ + 47^\circ) = 55^\circ$

Ejercicio 6

Paso 1: Calcular $\angle 1$

$\angle 1 = 180^\circ - (61^\circ + 68^\circ) = 51^\circ$

Paso 2: Calcular $\angle 2$

$\angle 2 = 180^\circ - 61^\circ = 119^\circ$

Paso 3: Calcular $\angle 3$

$\angle 3 = 180^\circ - (90^\circ + 61^\circ) = 29^\circ$

Ejercicio 7

Paso 1: Calcular $\angle 3$

$\angle 3 = \frac{180^\circ - 83^\circ}{2} = 48.5^\circ$

Paso 2: Calcular $\angle 1$

$\angle 1 = 180^\circ - (48^\circ + 48.5^\circ) = 83.5^\circ$

Paso 3: Calcular $\angle 4$

$\angle 4 = 180^\circ - 83^\circ = 97^\circ$

Paso 4: Calcular $\angle 2$

$\angle 2 = 180^\circ - (83.5^\circ + 48.5^\circ) = 48^\circ$

Answer:

1. $m\angle 1 = 73^\circ$, $m\angle 2 = 41^\circ$, $m\angle 3 = 96^\circ$
2. $m\angle 1 = 78^\circ$, $m\angle 2 = 47^\circ$, $m\angle 3 = 55^\circ$
3. $m\angle 1 = 51^\circ$, $m\angle 2 = 119^\circ$, $m\angle 3 = 29^\circ$
4. $m\angle 1 = 83.5^\circ$, $m\angle 2 = 48^\circ$, $m\angle 3 = 48.5^\circ$, $m\angle 4 = 97^\circ$