Question

n triangle ABC BE is perpendicular to AC angle EBC is equal to 40 degrees and angle BAC is equal to 30 degrees. Find the values of x, y, and z​

Answer 1

Answer:

Bruh, you didn't send the figure, I had to search it :/

Now, in ΔBEC,

Using Angle sum property,

∠EBC+∠ECB+∠ECB=180°

40+90+x=180

x=50°.

In ΔACD,

Using angle sum property,

∠DAC+∠ACD+∠CDA=180°

30+50+∠CDA=180°

∠CDA=100°.

Using linear pair,

∠ADB+∠CDA=180°

y+100°=180°

y=80°.

Using angle sum property,

∠ADB+∠DBE+∠DMB=180°.....( let the intersection point of AD and BE be M)

40+80+∠DMB=180

∠DMB=180-120

∠DMB=60°

Now, using vertically opposite angles,

∠DMB=z

z=60°.

THUS, x=50°, y=80°, z=60°.

HOPE THIS HELPS :D