Question

g.co.c.10: exterior angle theorem 1
1 in the diagram of $\triangle klm$ below, $m\angle l = 70$, $m\angle m = 50$, and $\overline{mk}$ is extended through $n$.
what is the measure of $\angle lkn$?

1. $60^\circ$
2. $120^\circ$
3. $180^\circ$
4. $300^\circ$

2 in the diagram below, $rcbt$ and $\triangle abc$ are shown with $m\angle a = 60$ and $m\angle abt = 125$.
what is $m\angle acr$?

1. $125$
2. $115$
3. $65$
4. $55$

3 given $\triangle abc$ with $m\angle b = 62^\circ$ and side $\overline{ac}$ extended to $d$, as shown below.
which value of $x$ makes $\overline{ab} \cong \overline{cb}$?

1. $59^\circ$
2. $62^\circ$
3. $118^\circ$
4. $121^\circ$

4 the measure of one of the base angles of an isosceles triangle is $42^\circ$. the measure of an exterior angle at the vertex of the triangle is

1. $42^\circ$
2. $84^\circ$
3. $96^\circ$
4. $138^\circ$

5 in $\triangle fgh$, $m\angle f = 42$ and an exterior angle at vertex $h$ has a measure of $104$. what is $m\angle g$?

1. $34$
2. $62$
3. $76$
4. $146$

Explanation:

Problem 1

Step1: Apply Exterior Angle Theorem

$\angle LKN = m\angle L + m\angle M$

Step2: Substitute given values

$\angle LKN = 70^\circ + 50^\circ = 120^\circ$

Problem 2

Step1: Find $\angle ABC$ first

$\angle ABC = 180^\circ - 125^\circ = 55^\circ$

Step2: Find $\angle ACB$ via triangle sum

$\angle ACB = 180^\circ - 60^\circ - 55^\circ = 65^\circ$

Step3: Find $\angle ACR$ (supplementary)

$\angle ACR = 180^\circ - 65^\circ = 65^\circ$

Problem 3

Step1: Identify base angles of isosceles $\triangle ABC$

If $\overline{AB} \cong \overline{CB}$, then $m\angle A = m\angle ACB$

Step2: Calculate $\angle ACB$ via triangle sum

$m\angle ACB = \frac{180^\circ - 62^\circ}{2} = 59^\circ$

Step3: Find $x$ (supplementary to $\angle ACB$)

$x = 180^\circ - 59^\circ = 121^\circ$

Problem 4

Step1: Calculate vertex angle of isosceles triangle

Vertex angle $= 180^\circ - 2\times42^\circ = 96^\circ$

Step2: Find exterior angle at vertex

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

Problem 5

Step1: Find interior $\angle H$

$\angle H = 180^\circ - 104^\circ = 76^\circ$

Step2: Calculate $\angle G$ via triangle sum

$\angle G = 180^\circ - 42^\circ - 76^\circ = 62^\circ$

Answer:

1. 2) $120^\circ$
2. 3) $65^\circ$
3. 4) $121^\circ$
4. 2) $84^\circ$
5. 2) $62^\circ$