Q:

need help solving with working much appreciated

Accepted Solution

A:
Answer:i. g = 70°ii. x = 85°Step-by-step explanation:Given:Let first we name the triangle i. ) Δ PQR , m∠ PRQ = 40°ii. ) Δ ABC is a right angle at B and a line B- D-C        m∠ DAC = 25°        m∠ ACD = 60°        m∠ BDA = x° To Find:i. g = ?ii. x = ?Solution:i.In Δ PQR , PR ≅ QR ...........{Given]∴ Δ PQR is an Isosceles Triangle.c.........{ Base angles of Isosceles triangle are equal }∴ m∠ PQR = m∠ RPQ = gNow sum of all the angles in a triangle is 180°∴ m∠ PQR + m∠ RPQ + m∠ PRQ = 180°....{Angle sum property of Triangle}[tex]g + g + 40 = 180\\2g=180-40\\2g=140\\g=\frac{140}{2} \\g=70\°[/tex]∴ g = 70°ii.We know sum of all the angles in a triangle is 180°In Δ DACm∠ DAC + m∠ ACD + m∠ ADC = 180°.....{Angle sum property of Triangle}[tex]25+60+ \angle ADC = 180\\[/tex][tex]\angle ADC = 180-85\\\angle ADC =95\\[/tex]Now By Linear Pair Angle Propertym∠ ADB + m∠ ADC = 180° ........{Linear Pair Angle Property}[tex]x+95=180\\x=180-95\\x=85[/tex]∴ x = 85°