Question

HELP!!! I am having trouble understanding how to do these problems. Can someone please help explain how to complete these problems. Thank you so much!

1. Find the measure of <6.


2. Find the measure of <4.

Answer 1

1=180 2=90

Explanation:

1=∠1 and ∠2 are supplementary, so m∠2 = 180° - x°. ∠2 and ∠6 are corresponding angles. So, m∠6 = 180° - x°.

2=Their measures are equal, so m∠4 = 90 . When two lines intersect to form one right angle, they form four right angles.

Answer 2

∠4 = 55°

∠6 = 35°

Explanation:

Finding the unknown angles:

In ΔABC,

35 + 90 + ∠4 = 180° {Sum of all angles of triangle}

125 +∠4 = 180

∠4 = 180 - 125

∠4 = 55°

Linear pair: If in two adjacent angles, the non-common arms form a straight line, then the two angles are called linear pair and they add up to 180.

∠7 + ∠8 = 180° {linear pair}

90 + ∠7 = 180°

∠7 = 180 - 90

∠7 = 90°

In ΔACD,

∠6 + ∠4+ ∠7 = 180 {Sum of all angles of triangle}

∠6 + 55 + 90 = 180

∠6 + 145 = 180

∠6 = 180 - 145

∠6 = 35°