Question

100 POINTS

Work out with working out, explanation, rules + formulae, please!

Answer 1

Answer :

• θ = 52°

Explanation :

In Δ XBC,

• m∠CXB = m∠B ( base angles of isosceles triangle are equal in measure )

thus,

• m∠CXB + m∠B + m∠C = 180°
• m∠CXB + m∠CXB + 58° = 180°
• 2m∠CXB + 58° = 180°
• 2m∠CXB = 180° - 58°
• 2m∠CXB = 122°
• m∠CXB = 122°/2
• m∠CXB = 61°

In line AB ,

• m∠AXY + m∠YXC + m∠CXB = 180° ( measure of a straight line is equal to 180° )
• 67° + θ + 61° = 180°
• θ + 128° = 180°
• θ = 180° - 128°
• θ = 52°