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Math  /  Geometry

Questionp=q=r=s=\begin{array}{l}\mathrm{p}= \\ \mathrm{q}= \\ \mathrm{r}= \\ \mathrm{s}=\end{array}

Studdy Solution

STEP 1

1. The sum of angles on a straight line is 180∘180^\circ.
2. Vertical angles (opposite angles) are equal.

STEP 2

1. Determine the value of angle pp.
2. Determine the value of angle qq.
3. Determine the value of angle rr.
4. Determine the value of angle ss.

STEP 3

Given that the angle adjacent to pp is 120∘120^\circ, use the fact that the sum of angles on a straight line is 180∘180^\circ. Therefore, calculate pp as:
p=180∘−120∘ p = 180^\circ - 120^\circ

STEP 4

Calculate the value of pp:
p=60∘ p = 60^\circ

STEP 5

Given that the angle adjacent to qq is 130∘130^\circ, use the fact that the sum of angles on a straight line is 180∘180^\circ. Therefore, calculate qq as:
q=180∘−130∘ q = 180^\circ - 130^\circ

STEP 6

Calculate the value of qq:
q=50∘ q = 50^\circ

STEP 7

Since rr is vertically opposite to the angle labeled 100∘100^\circ, use the property that vertical angles are equal. Therefore, rr is:
r=100∘ r = 100^\circ

STEP 8

Since ss is vertically opposite to the angle labeled 130∘130^\circ, use the property that vertical angles are equal. Therefore, ss is:
s=130∘ s = 130^\circ
The measures of the angles are: p=60∘,q=50∘,r=100∘,s=130∘ p = 60^\circ, \quad q = 50^\circ, \quad r = 100^\circ, \quad s = 130^\circ

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