Question

unit 5: the angle sum of a quadrilateral
question 1 find the value of each pronumeral.
question 2 find the unknown angles.
question 3 find the value of the following pronumerals.

Explanation:

Step1: Recall angle - sum property

The sum of interior angles of a quadrilateral is $360^{\circ}$.

Step2: Solve for x in part a of Question 1

We have the equation $50 + 120+110 + x=360$.
Combining like - terms: $280 + x=360$.
Subtracting 280 from both sides: $x = 360 - 280=80$.

Step3: Solve for m in part b of Question 1

Using the angle - sum property, $60 + 90+140 + m=360$.
Combining like - terms: $290 + m=360$.
Subtracting 290 from both sides: $m = 360 - 290 = 70$.

Step4: Solve for x in part c of Question 1

We know that $90+75 + 80+x=360$.
Combining like - terms: $245+x=360$.
Subtracting 245 from both sides: $x=360 - 245 = 115$.

Step5: Solve for x and y in part d of Question 1

Since the two lines are parallel, the co - interior angles are supplementary.
For the pair of co - interior angles involving $x$ and $100^{\circ}$, $x + 100=180$, so $x = 80$.
For the other pair involving $y$ and $58^{\circ}$, $y+58 = 180$, so $y = 122$.

Step6: Solve for x in part e of Question 1

In a parallelogram, opposite angles are equal. So $x = 60$.

Step7: Solve for x in part f of Question 1

Since all angles in the quadrilateral are equal and their sum is $360^{\circ}$, $4x=360$, so $x = 90$.

Answer:

Question 1:
a. $x = 80$
b. $m = 70$
c. $x = 115$
d. $x = 80$, $y = 122$
e. $x = 60$
f. $x = 90$

(We can continue to solve Question 2 and Question 3 in a similar fashion using the angle - sum properties of polygons and other geometric relationships as needed.)