Question

AB is a straight line. XYZ is an isosceles triangle. A What is the value of angle m? A 120° B 95° C 60° D 85° E 75°​

Answer 1

Answer is E. 75 degree angle

Step by step

An isosceles triangle has two equal angles. Since we know one is 90, the other two sum will be 90 to equal total 180.
90/2 = 45 each angle.

The straight angle AB will sum 180 degrees. We now know one angle is 45, the given angle is 60.
180 - 45 - 60 = 75 degrees. Angle M = 75 degrees.

Answer 2

AB is a straight line ⇒ m(∡BXA) = 180°

m(∡BXA) = m(∡BXY) + m(∡YXA) ⇔

⇔ 180° = 60° + m(∡YXA) ⇔

⇔ 60° + m(∡YXA) = 180° ⇔

⇔ m(∡YXA) = 180° - 60° ⇒ m(∡YXA) = 120°

∆XYZ is an isosceles triangle and has an angle of 90° ⇒ m(∡ZXY) = m(∡XYZ) = 45°, because a triangle has 180°

m = m(∡AXZ) ⇒ m(∡AXZ) = ?

m(∡BXA) = m(∡BXY) + m(∡YXZ) + m(∡AXZ) ⇔

⇔ 180° = 60° + 45° + m(∡AXZ) ⇔

⇔ 105° + m(∡AXZ) = 180° ⇔

⇔ m(∡AXZ) = 180° - 105° ⇒ m(∡AXZ) = 75° ⇔

⇔ m = 75°

Good luck! :)