Question

6.8a practice 1
extending previous knowledge of triangles (angles)
1 triangle hjk is shown.
a) measure of $angle hjk$ = ________
b) $angle$ ________ is opposite side $overline{hj}$.
c) $angle$ ________ is opposite side $overline{jk}$.
d) $angle$ ________ is opposite side $overline{hk}$.
2 triangle pqr is shown.
a) measure of $angle pqr$ = ________
b) $angle$ ________ is opposite side $overline{rp}$.
c) $angle$ ________ is opposite side $overline{rq}$.
d) $angle$ ________ is opposite side $overline{pq}$.
3 in triangle klm, the measure of angle lmk is $45^circ$ and the measure of angle klm is $85^circ$. what is the measure of angle mkl in degrees?
a) measure of $angle mkl$ = ________
b) $angle$ ________ is opposite side $overline{kl}$.
c) $angle$ ________ is opposite side $overline{lm}$.
d) $angle$ ________ is opposite side $overline{mk}$.

Explanation:

Step1: Calculate ∠HJK (Triangle HJK)

Sum of angles in a triangle is $180^\circ$.
$\angle HJK = 180^\circ - 90^\circ - 58^\circ = 32^\circ$

Step2: Identify opposite angles (HJK)

• Side $\overline{HJ}$ is opposite $\angle K$
• Side $\overline{JK}$ is opposite $\angle H$
• Side $\overline{HK}$ is opposite $\angle J$

Step3: Calculate ∠PQR (Triangle PQR)

Sum of angles in a triangle is $180^\circ$.
$\angle PQR = 180^\circ - 42^\circ - 84^\circ = 54^\circ$

Step4: Identify opposite angles (PQR)

• Side $\overline{RP}$ is opposite $\angle Q$
• Side $\overline{RQ}$ is opposite $\angle P$
• Side $\overline{PQ}$ is opposite $\angle R$

Step5: Calculate ∠MKL (Triangle KLM)

Sum of angles in a triangle is $180^\circ$.
$\angle MKL = 180^\circ - 45^\circ - 85^\circ = 50^\circ$

Step6: Identify opposite angles (KLM)

• Side $\overline{KL}$ is opposite $\angle M$
• Side $\overline{LM}$ is opposite $\angle K$
• Side $\overline{MK}$ is opposite $\angle L$

Answer:

1. Triangle HJK

a) $32^\circ$
b) $\angle K$
c) $\angle H$
d) $\angle J$

2. Triangle PQR

a) $54^\circ$
b) $\angle Q$
c) $\angle P$
d) $\angle R$

3. Triangle KLM

a) $50^\circ$
b) $\angle M$ (or $\angle LMK$)
c) $\angle K$ (or $\angle MKL$)
d) $\angle L$ (or $\angle KLM$)