Point Z is the circumcenter of triangle T U V. Lines are drawn from each point of the triangle to point Z. Lines are drawn from point Z to each side to form right angles and line segments Z A, Z B, and Z C. The line segments cut the sides into 2 equal parts. ∠ZTB is 32.8° and ∠BZU is 57.2°. What is m∠ZUB?

Solution:

From triangle BZU, 

∠ZBU + ∠ZUB + ∠BZU = 180°

90° + ∠ZUB + 57.2° = 180°

∠ZUB = 32.8°

Aliter 

From figure ZT and ZU are the radius of the circle. Hence they are equal lengths.

∴ ΔZTU is an isosceles triangle and also from property of triangle which states that “angles opposite to equal sides of triangle are equal”.

We can conclude ∠ZTB = ∠ZUB = 32.8° since these are angle opposite to equal sides, ZT and ZU.

Point Z is the circumcenter of triangle T U V. Lines are drawn from each point of the triangle to point Z. Lines are drawn from point Z to each side to form right angles and line segments Z A, Z B, and Z C. The line segments cut the sides into 2 equal parts. ∠ZTB is 32.8° and ∠BZU is 57.2°. What is m∠ZUB?

Summary:

Given , Point Z is the circumcenter of triangle T U V. Lines are drawn from each point of the triangle to point Z. Lines are drawn from point Z to each side to form right angles and line segments Z A, Z B, and Z C. The line segments cut the sides into 2 equal parts. ∠ZTB is 32.8° and ∠BZU is 57.2°. The value of ∠ZUB is 32.8°.