Question

1. if ( mangle4 = 35 ), find ( mangle3 ). explain.

a. 145; ( angle3 ) and ( angle4 ) are supplementary angles, so ( mangle3 = 180 - mangle4 ).
b. 55; ( angle3 ) and ( angle4 ) are complementary angles, so ( mangle3 = 90 - mangle4 ).
c. 35; ( angle3 ) and ( angle4 ) are corresponding angles, so ( mangle3 = mangle4 ).
d. 35; ( angle3 ) and ( angle4 ) are alternate interior angles, so ( mangle3 = mangle4 ).

Explanation:

Step1: Determine the relationship between ∠3 and ∠4

From the figure, ∠3 and ∠4 are complementary angles (they form a right - angle together).

Step2: Calculate \(m\angle3\)

Since \(m\angle3 + m\angle4=90^{\circ}\) (complementary angles sum to \(90^{\circ}\)), and \(m\angle4 = 35^{\circ}\), then \(m\angle3=90 - m\angle4\).
Substitute \(m\angle4 = 35^{\circ}\) into the formula: \(m\angle3=90 - 35\).

Answer:

B. 55; \(\angle3\) and \(\angle4\) are complementary angles, so \(m\angle3 = 90 - m\angle4\).