Question

13. In the following is 9.74, use the information given to find the measures p and q
Then find the sum of p and q
​

Answer 1

• Measure of p is 130°.
• Measure of q is 50°
• Sum of p and q is 180°.

Step-by-step explanation:

To find:-

• Sum of p and q.
• Measure of p.
• Measure of q.

Solution:-

According to given figure,

Two lines are parallel and both lines are interesting by an transversal.

We know,

Sum of all angles forms on straight line is equal to 180°. This statement is known as linear pair.

So,

➝ ∠p + 50° = 180°

➝ ∠p = 180° - 50°

➝ ∠p = 130°

We also know,

Sum of two adjacent angles forms when two lines are parallel and both lines is intersect by an transversal is equal to 180°. This statement is known as Co-interior angles.

So,

➝ ∠p + ∠q = 180°

➝ 130° + ∠q = 180°

➝ ∠q = 180° - 130°

➝ ∠q = 50°.

Therefore,

Measure of p is 130°.

Measure of q is 50°.

Sum of p and q = 130° + 50° = 180°

Answer 2

$\huge\mathfrak{{\fcolorbox{orange}{orange}{Answer~~~~~↓}}}$

$\small{ }$

$\large\bold{{\underline{\underline{\orange{To~find:}}}}}$

The unknown angles ‛p’ and ‛q’

Given, The two lines are parallel..

$\implies\mathtt{q={\underline{\underline{50°}}}}$ (Alternate Interior Angles)

$\large\bold{{\underline{\underline{\orange{Also:}}}}}$

$\implies\mathtt{p+50°=180°}$ (Linear pair)

$\implies\mathtt{p=180-50}$

$\implies\mathtt{p={\underline{\underline{130°}}}}$

$\small{ }$

$\large\therefore\bold{{\underline{\underline{\orange{Required~answer:}}}}}$

• p = 130°
• q = 50°

$\small{ }$

$\huge\bold\orange{★Hope~it~helps..!!}$