Question

BRAINLIEST!! HELP!!
In the figure, p || q . Find m<1

Answer 1

Answer:

  $m\angle 1=70^o$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

In the triangle SAB

$m\angle ASB+m\angle SAB+m\angle SBA=180^o$

Find the measure of angle ASB

we know that

$m\angle ASB+116^o=180^o$ ----> by supplementary angles (form a linear pair)

$m\angle ASB=180^o-116^o=64^o$

Find the measure of angle SBA

we know that

$m\angle SBC=134^o$ ----> by corresponding angles

Remember that

$m\angle SBA+m\angle SBC=180^o$ ---> by supplementary angles (form a linear pair)

substitute

$m\angle SBA+134^o=180^o$

$m\angle SBA=180^o-134^o=46^o$

Find the measure of angle SAB

$m\angle ASB+m\angle SAB+m\angle SBA=180^o$

substitute

$64^o+m\angle SAB+46^o=180^o$

$m\angle SAB=180^o-110^o=70^o$

Find the measure of angle 1

we know that

$m\angle 1=m\angle SAB$ ----> by vertical angles

therefore

$m\angle 1=70^o$