In the figure below, line OP is parallel to line RS. Angle OPR is twice angle PRS. Find the size of angle OPR. 13. During a football tournament, a team scored the following goals in different matches: 8, 5, 6, 5, 4 and 2. Find the mean number of goals scored per match.

Kwa kuwa laini $OP$ inalingana na laini $RS$ ($OP \parallel RS$), na $PR$ ni laini inayokatisha (transversal), pembe $\angle OPR$ na $\angle PRS$ ni pembe za ndani zinazoelekeana (consecutive interior angles). Hizi pembe hujumlisha hadi $180^\circ$.
Hivyo, $\angle OPR + \angle PRS = 180^\circ$.

Tunajua kwamba $\angle OPR = 2 \times \angle PRS$.
Wacha $\angle PRS = x$.
Basi, $\angle OPR = 2x$.
Badilisha hizi kwenye mlinganyo wa Step 1:

Tunajua $\angle OPR = 2x$.

Ukubwa wa pembe OPR ni $\boxed{\text{}120^\circ\text{}}$.

13. Wakati wa mashindano ya mpira wa miguu, timu ilifunga magoli yafuatayo katika mechi tofauti: 8, 5, 6, 5, 4 na 2. Tafuta wastani wa idadi ya magoli yaliyofungwa kwa kila mechi.

Jumla ya magoli = $8 + 5 + 6 + 5 + 4 + 2$

Kuna idadi ya magoli 6 yaliyotolewa, kwa hivyo kuna mechi 6.

Wastani = $\frac{\text{Jumla ya magoli}}{\text{Idadi ya mechi}}$

Wastani wa idadi ya magoli yaliyofungwa kwa kila mechi ni $\boxed{\text{}5\text{}}$.